JP6282325B2 - Receiving apparatus and receiving method - Google Patents

Description

  The present invention relates to a receiving apparatus and a receiving method using a low density parity check convolutional code (LDPC-CC) that can support a plurality of coding rates.

  In recent years, attention has been focused on a low-density parity check (LDPC) code as an error correction code that exhibits high error correction capability with a feasible circuit scale. Since the LDPC code has a high error correction capability and is easy to implement, the LDPC code is adopted in an error correction coding system such as an IEEE802.11n high-speed wireless LAN system or a digital broadcasting system.

  The LDPC code is an error correction code defined by a low-density parity check matrix H. Also, the LDPC code is a block code having a block length equal to the number N of columns of the check matrix H. For example, Non-Patent Document 1, Non-Patent Document 2, Non-Patent Document 3, and Non-Patent Document 4 propose a random LDPC code, Array LDPC code, and QC-LDPC code (QC: Quasi-Cyclic).

  However, many of the current communication systems are characterized in that transmission information is collectively transmitted for each variable-length packet or frame, as in Ethernet (registered trademark). When an LDPC code, which is a block code, is applied to such a system, for example, there is a problem of how a block of a fixed-length LDPC code corresponds to a variable-length Ethernet (registered trademark) frame. In IEEE802.11n, the length of the transmission information sequence and the block length of the LDPC code are adjusted by performing padding processing and puncturing processing on the transmission information sequence. It is difficult to avoid transmitting redundant sequences.

  An LDPC code of such a block code (hereinafter referred to as LDPC-BC: Low-Density Parity-Check Block Code) can be encoded / decoded for an information sequence of an arbitrary length. Possible LDPC-CC (Low-Density Parity-Check Convolutional Codes) has been studied (for example, see Non-Patent Document 1 and Non-Patent Document 2).

LDPC-CC is a convolutional code defined by a low-density parity check matrix. For example, an LDPC-CC parity check matrix H ^T [0, n] with a coding rate R = 1/2 (= b / c). Is shown in FIG. Here, the element h ₁ ^(m) (t) of H ^T [0, n] takes 0 or 1. All elements other than h ₁ ^(m) (t) are 0. M represents the memory length in LDPC-CC, and n represents the length of the LDPC-CC codeword. As shown in FIG. 1, in the LDPC-CC parity check matrix, 1 is arranged only in the diagonal term of the matrix and its neighboring elements, the lower left and upper right elements of the matrix are zero, and a parallelogram It has the feature of being a type matrix.

Here, when h ₁ ⁽⁰⁾ (t) = 1, h ₂ ⁽⁰⁾ (t) = 1, the LDPC-CC encoder defined by the parity check matrix H ^T [0, n] T is This is shown in FIG. As shown in FIG. 2, the LDPC-CC encoder includes a shift register M + 1 having a bit length c and a mod2 adder (exclusive OR operation) unit. For this reason, the LDPC-CC encoder is realized by a very simple circuit compared to a circuit that performs multiplication of a generator matrix and an LDPC-BC encoder that performs an operation based on the backward (forward) substitution method. There is a feature that can be. Further, since FIG. 2 shows a convolutional code encoder, it is not necessary to encode an information sequence by dividing it into fixed-length blocks, and an information sequence of an arbitrary length can be encoded.

R. G. Gallager, “Low-density parity check codes,” IRE Trans. Inform. Theory, IT-8, pp-21-28, 1962. D. J. C. Mackay, “Good error-correcting codes based on very sparse matrices,” IEEE Trans. Inform. Theory, vol.45, no.2, pp399-431, March 1999. J. L. Fan, “Array codes as low-density parity-check codes,” proc. Of 2nd Int. Symp. On Turbo Codes, pp.543-546, Sep. 2000. M. P. C. Fossorier, “Quasi-cyclic low-density parity-check codes from circulant permutation matrices,” IEEE Trans. Inform. Theory, vol.50, no.8, pp.1788-1793, Nov. 2001. MPC Fossorier, M. Mihaljevic, and H. Imai, “Reduced complexity iterative decoding of low density parity check codes based on belief propagation,” IEEE Trans. Commun., Vol.47., No.5, pp.673-680, May 1999. J. Chen, A. Dholakia, E. Eleftheriou, MPC Fossorier, and X.-Yu Hu, “Reduced-complexity decoding of LDPC codes,” IEEE Trans. Commun., Vol.53., No.8, pp.1288 -1299, Aug. 2005. J. Zhang, and M. P. C. Fossorier, “Shuffled iterative decoding,” IEEE Trans. Commun., Vol.53, no.2, pp.209-213, Feb. 2005. S. Lin, D. J. Jr., Costello, “Error control coding: Fundamentals and applications,” Prentice-Hall. Tadashi Wadayama, “Low-density parity check code and its decoding method,” Trikes.

  However, sufficient studies have not been made on LDPC-CC having a plurality of coding rates, a low computation scale, and good data reception quality, and its encoder and decoder.

  For example, Non-Patent Document 8 shows that puncturing is used to cope with a plurality of coding rates. When dealing with a plurality of coding rates using punctures, first, a base code, that is, a mother code is prepared, an encoded sequence in the mother code is created, and transmission is not performed from the encoded sequence (puncture). Select a bit. By changing the number of bits that are not transmitted, a plurality of coding rates are supported. As a result, both the encoder and the decoder can cope with all coding rates by using the encoder and decoder for the mother code, which has the advantage that the operation scale (circuit scale) can be reduced. .

  On the other hand, as a method of dealing with a plurality of coding rates, there is a method of preparing different codes for each coding rate (Distributed Codes). In particular, in the case of an LDPC code, it is described in Non-Patent Document 9. In other words, a method of dealing with a plurality of coding rates with a plurality of codes is general because of the flexibility of easily configuring various code lengths and coding rates. At this time, since a plurality of codes are used, there is a disadvantage that the operation scale (circuit scale) is large, but the data reception quality is very good as compared with the case where a plurality of coding rates are supported by puncturing. With advantages.

  In consideration of the above points, the operation scale of the encoder and the decoder is ensured while ensuring the reception quality of the data by preparing a plurality of codes to cope with a plurality of coding rates. There are few references discussing LDPC code generation methods that can reduce the amount of data, and if an LDPC code creation method that can achieve this is established, improvement of data reception quality and reduction of the computation scale, which have been difficult to achieve until now, have been achieved. Coexistence is possible.

  Also, since LDPC-CC is a kind of convolutional code, termination and tail biting are required to ensure reliability in decoding information bits. However, sufficient studies have not been made on LDPC-CC and its encoder and decoder that can reduce the number of terminations as much as possible while ensuring the data reception quality.

  An object of the present invention is to prevent deterioration of error transmission efficiency and avoid deterioration of information transmission efficiency even when termination is performed in an encoder and a decoder using LDPC-CC. It is to provide a receiving apparatus and a receiving method.

  The receiving apparatus of the present invention is generated by an encoding operation using a low density parity check convolutional code (LDPC-CC) for an information sequence composed of a plurality of bits and known information added to the information sequence. The length of the known information is determined according to a receiving unit that receives a signal including a parity bit and the information sequence, and a coding rate used in the LDPC-CC coding calculation included in the received signal. A likelihood that generates a likelihood corresponding to the known information according to a length of the control information generation unit and the known information, and generates a likelihood of the information sequence and a likelihood of the parity bit from the received signal. A degree ratio generation unit, a decoding unit that decodes the information sequence by performing a decoding operation using a likelihood of the information sequence, a likelihood of the parity bit, and a likelihood corresponding to the known information; The A configuration that.

  The reception method of the present invention is generated by encoding operation using a low density parity check convolutional code (LDPC-CC) for an information sequence composed of a plurality of bits and known information added to the information sequence. A signal including the parity bit and the information series is received, and a length of the known information is determined according to a coding rate used in the LDPC-CC coding operation included in the received signal, and the known information is determined. According to the length of the information, the likelihood corresponding to the known information is generated, the likelihood of the information sequence, the likelihood of the parity bit is generated from the received signal, the likelihood of the information sequence, A configuration is adopted in which the information sequence is decoded by performing a decoding operation using the likelihood of the parity bit and the likelihood corresponding to the known information.

  According to the present invention, even when termination is performed, the error correction capability is not degraded, and a decrease in information transmission efficiency can be avoided.

The figure which shows the check matrix of LDPC-CC The figure which shows the structure of a LDPC-CC encoder. The figure which shows an example of a structure of the check matrix of LDPC-CC of time-varying period 4 The figure which shows the structure of the parity check polynomial and check matrix H of LDPC-CC of time-varying period 3 The figure which shows the relationship of the reliability propagation | transmission of each term regarding X (D) of "check type | formula # 1"-"check type | formula # 3" of FIG. 4A The figure which shows the relationship of the reliability propagation | transmission of each item regarding X (D) of "check type | formula # 1"-"check type | formula # 6" The figure which shows the check matrix of a (7,5) convolutional code. The figure which shows an example of a structure of the check matrix H of LDPC-CC of coding rate 2/3 and time-varying period 2 The figure which shows an example of a structure of the parity check matrix of LDPC-CC of coding rate 2/3 and time-varying period m The figure which shows an example of a structure of the parity check matrix of LDPC-CC of coding rate (n-1) / n and time-varying period m. The figure which shows an example of a structure of a LDPC-CC encoding part. Illustration for explaining the "Information-zero-termination" method The block diagram which shows the principal part structure of the encoder based on Embodiment 3 of this invention. The block diagram which shows the principal part structure of the 1st information calculating part which concerns on Embodiment 3. FIG. FIG. 9 is a block diagram showing a main configuration of a parity operation unit according to the third embodiment. FIG. 9 is a block diagram showing another main configuration of the encoder according to Embodiment 3. FIG. 9 is a block diagram showing a main configuration of a decoder according to the third embodiment. The figure for demonstrating operation | movement of the log likelihood ratio setting part in the case of coding rate 1/2. The figure for demonstrating operation | movement of the log likelihood ratio setting part in the case of coding rate 2/3. The figure which shows an example of a structure of the communication apparatus carrying the encoder which concerns on Embodiment 3. FIG. Diagram showing an example of transmission format The figure which shows an example of a structure of the communication apparatus carrying the decoder which concerns on Embodiment 3. FIG. The figure which shows an example of the relationship between information size and the number of terminations The figure which shows another example of the relationship between information size and the number of terminations The figure which shows an example of the relationship between information size and the number of terminations The block diagram which shows the principal part structure of the communication apparatus carrying the encoder which concerns on Embodiment 5 of this invention. Diagram for explaining how to determine the termination sequence length Diagram for explaining how to determine the termination sequence length Diagram showing an example of transmission format FIG. 7 is a block diagram showing a main configuration of a communication apparatus equipped with a decoder according to the fifth embodiment. The figure which shows an example of the flow of the information between the communication apparatus which mounts an encoder, and the communication apparatus which mounts a decoder The figure which shows an example of the flow of the information between the communication apparatus which mounts an encoder, and the communication apparatus which mounts a decoder The figure which shows an example of the correspondence table which shows the relationship between information size and the number of terminations The figure which shows the BER / BLER characteristic at the time of adding a termination series to the information series whose information size is 512 bits The figure which shows the BER / BLER characteristic at the time of adding a termination series to the information series whose information size is 1024 bits The figure which shows the BER / BLER characteristic at the time of adding a termination series to the information series whose information size is 2048 bits The figure which shows the BER / BLER characteristic at the time of adding a termination series to the information series whose information size is 4096 bits The figure which shows the correspondence table of information size and support coding rate The block diagram which shows the principal part structure of the communication apparatus carrying the encoder which concerns on Embodiment 6 of this invention. The figure which shows an example of the flow of the information between the communication apparatus which mounts an encoder, and the communication apparatus which mounts a decoder FIG. 9 is a block diagram showing a main configuration of a communication apparatus equipped with a decoder according to the sixth embodiment. The block diagram which shows the principal part structure of the encoder based on Embodiment 7 of this invention The block diagram which shows the principal part structure of the decoder which concerns on Embodiment 7. The block diagram which shows the principal part structure of the encoder which concerns on Embodiment 8 of this invention.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

(Embodiment 1)
First, in this embodiment, an LDPC-CC having good characteristics will be described.

(LDPC-CC with good characteristics)
The LDPC-CC having a time varying period g with good characteristics will be described below.

  First, an LDPC-CC having a time varying period of 4 with good characteristics will be described. In the following, a case where the coding rate is 1/2 will be described as an example.

Formulas (1-1) to (1-4) are considered as parity check polynomials for LDPC-CC with a time-varying period of 4. At this time, X (D) is a polynomial expression of data (information), and P (D) is a polynomial expression of parity. Here, in the equations (1-1) to (1-4), the parity check polynomial is such that four terms exist in each of X (D) and P (D). This is because it is preferable to obtain four terms.

In Expression (1-1), a1, a2, a3, and a4 are integers (however, a1 ≠ a2 ≠ a3 ≠ a4, and all of a1 to a4 are different). In the following, when “X ≠ Y ≠... ≠ Z”, X, Y,..., Z are all different from each other. B1, b2, b3, and b4 are integers (where b1 ≠ b2 ≠ b3 ≠ b4). The parity check polynomial of equation (1-1) is referred to as “check equation # 1”, and a sub-matrix based on the parity check polynomial of equation (1-1) is referred to as a first sub-matrix H ₁ .

In the formula (1-2), A1, A2, A3, and A4 are integers (however, A1 ≠ A2 ≠ A3 ≠ A4). B1, B2, B3, and B4 are integers (B1 ≠ B2 ≠ B3 ≠ B4). Referred to parity check polynomial of equation (1-2) and "check equation # 2", the sub-matrix based on a parity check polynomial of equation (1-2), the second sub-matrix H _2.

In Expression (1-3), α1, α2, α3, and α4 are integers (where α1 ≠ α2 ≠ α3 ≠ α4). Β1, β2, β3, and β4 are integers (where β1 ≠ β2 ≠ β3 ≠ β4). The parity check polynomial of equation (1-3) is called “check equation # 3”, and the sub-matrix based on the parity check polynomial of equation (1-3) is referred to as a third sub-matrix H ₃ .

In the formula (1-4), E1, E2, E3, and E4 are integers (however, E1 ≠ E2 ≠ E3 ≠ E4). Further, F1, F2, F3, and F4 are integers (where F1 ≠ F2 ≠ F3 ≠ F4). The parity check polynomial of equation (1-4) is called “check equation # 4”, and the sub-matrix based on the parity check polynomial of equation (1-4) is referred to as a fourth sub-matrix H ₄ .

The first sub-matrix _{H 1,} second sub-matrix _{H 2,} third sub-matrix _{H 3,} fourth sub-matrix _{H 4,} the LDPC-CC of varying period 4 when generating a check matrix as shown in FIG. 3 Think.

  At this time, in the formulas (1-1) to (1-4), combinations of orders of X (D) and P (D) (a1, a2, a3, a4), (b1, b2, b3, b4), (A1, A2, A3, A4), (B1, B2, B3, B4), (α1, α2, α3, α4), (β1, β2, β3, β4), (E1, E2, E3, E4), When the remainder obtained by dividing each value of (F1, F2, F3, F4) by 4 is k, the remainder is divided into four coefficient sets (for example, (a1, a2, a3, a4)) expressed as described above. 0, 1, 2, and 3 are included one by one, and all four coefficient sets are satisfied.

  For example, if each order (a1, a2, a3, a4) of X (D) of “check formula # 1” is (a1, a2, a3, a4) = (8, 7, 6, 5), each order The remainder k obtained by dividing (a1, a2, a3, a4) by 4 becomes (0, 3, 2, 1), and the remainder (k) 0, 1, 2, 3 is one by one in the four coefficient sets. To be included. Similarly, if each order (b1, b2, b3, b4) of P (D) of “inspection formula # 1” is (b1, b2, b3, b4) = (4, 3, 2, 1), The remainder k obtained by dividing the order (b1, b2, b3, b4) by 4 becomes (0, 3, 2, 1), and 0, 1, 2, 3 are obtained as the remainder (k) in the four coefficient sets. It will be included one by one. For the four coefficient sets of X (D) and P (D) of other inspection formulas (“check formula # 2”, “check formula # 3”, “check formula # 4”), the above “remainder” is also related. It is assumed that the condition is satisfied.

  By doing in this way, it becomes possible to form a regular LDPC code in which the column weight of the parity check matrix H composed of the expressions (1-1) to (1-4) is 4 in all columns. . Here, the regular LDPC code is an LDPC code defined by a parity check matrix in which each column weight is constant, and has characteristics that characteristics are stable and an error floor is difficult to occur. In particular, when the column weight is 4, the characteristics are good. Therefore, by generating the LDPC-CC as described above, it is possible to obtain the LDPC-CC with good reception performance.

Table 1 is an example of LDPC-CC (LDPC-CC # 1 to # 3) having a time-varying period of 4 and a coding rate of ½, in which the condition regarding the “remainder” is satisfied. In Table 1, an LDPC-CC having a time varying period of 4 is defined by four parity check polynomials of “check polynomial # 1”, “check polynomial # 2”, “check polynomial # 3”, and “check polynomial # 4”. The

  In the above description, the case where the coding rate is 1/2 has been described as an example. However, when the coding rate is (n−1) / n, information X1 (D), X2 (D),... Xn− In each of the four coefficient sets in 1 (D), if the above-mentioned condition relating to the “remainder” is satisfied, it becomes a regular LDPC code, and good reception quality can be obtained.

  Even in the case of time-varying period 2, it was confirmed that a code with good characteristics can be searched by applying the condition relating to the “remainder”. Hereinafter, an LDPC-CC having a time-varying period 2 with good characteristics will be described. In the following, a case where the coding rate is 1/2 will be described as an example.

As LDPC-CC parity check polynomials with a time-varying period of 2, equations (2-1) and (2-2) are considered. At this time, X (D) is a polynomial expression of data (information), and P (D) is a polynomial expression of parity. Here, in equations (2-1) and (2-2), the parity check polynomial is such that four terms exist in each of X (D) and P (D). This is because it is preferable to obtain four terms.

In Expression (2-1), a1, a2, a3, and a4 are integers (where a1 ≠ a2 ≠ a3 ≠ a4). B1, b2, b3, and b4 are integers (where b1 ≠ b2 ≠ b3 ≠ b4). The parity check polynomial of equation (2-1) is referred to as “check equation # 1”, and the sub-matrix based on the parity check polynomial of equation (2-1) is referred to as a first sub-matrix H ₁ .

In the formula (2-2), A1, A2, A3, and A4 are integers (however, A1 ≠ A2 ≠ A3 ≠ A4). B1, B2, B3, and B4 are integers (B1 ≠ B2 ≠ B3 ≠ B4). Referred to parity check polynomial of equation (2-2) and "check equation # 2", the sub-matrix based on a parity check polynomial of equation (2-2), the second sub-matrix H _2.

Then, consider a time-varying period 2 LDPC-CC generated from the first sub-matrix H ₁ and the second sub-matrix H ₂ .

  At this time, in the formulas (2-1) and (2-2), combinations of orders of X (D) and P (D) (a1, a2, a3, a4), (b1, b2, b3, b4), When the remainder obtained by dividing each value of (A1, A2, A3, A4), (B1, B2, B3, B4) by 4 is k, four coefficient sets (e.g., (a1, a2, a3, a4)) include one remainder, 0, 1, 2 and 3, and all four coefficient sets are satisfied.

  For example, if each order (a1, a2, a3, a4) of X (D) of “check formula # 1” is (a1, a2, a3, a4) = (8, 7, 6, 5), each order The remainder k obtained by dividing (a1, a2, a3, a4) by 4 becomes (0, 3, 2, 1), and the remainder (k) 0, 1, 2, 3 is one by one in the four coefficient sets. To be included. Similarly, if each order (b1, b2, b3, b4) of P (D) of “inspection formula # 1” is (b1, b2, b3, b4) = (4, 3, 2, 1), The remainder k obtained by dividing the order (b1, b2, b3, b4) by 4 becomes (0, 3, 2, 1), and 0, 1, 2, 3 are obtained as the remainder (k) in the four coefficient sets. It will be included one by one. It is assumed that the condition regarding the “remainder” is also satisfied for each of the four coefficient sets of X (D) and P (D) of “inspection formula # 2.”

  By doing in this way, it becomes possible to form a regular LDPC code in which the column weights of the parity check matrix H composed of equations (2-1) and (2-2) are 4 in all columns. . Here, the regular LDPC code is an LDPC code defined by a parity check matrix in which each column weight is constant, and has characteristics that characteristics are stable and an error floor is difficult to occur. In particular, when the row weight is 8, since the characteristics are good, by generating the LDPC-CC as described above, it is possible to obtain the LDPC-CC that can further improve the reception performance. Become.

Table 2 shows an example of LDPC-CC (LDPC-CC # 1, # 2) with a time-varying period of 2 and a coding rate of ½, where the condition regarding the “remainder” is satisfied. In Table 2, the LDPC-CC with time-varying period 2 is defined by two parity check polynomials of “check polynomial # 1” and “check polynomial # 2”.

  In the above description (LDPC-CC with time-varying period 2), the case where the coding rate is 1/2 has been described as an example, but when the coding rate is (n-1) / n, the information X1 (D), In each of the four coefficient sets in X2 (D),..., Xn-1 (D), if the above-mentioned condition relating to “remainder” is satisfied, it becomes a regular LDPC code, and good reception quality can be obtained. it can.

  In addition, even in the case of the time-varying period 3, it was confirmed that a code having good characteristics can be searched by applying the following condition regarding “remainder”. Hereinafter, an LDPC-CC having a time varying period of 3 with good characteristics will be described. In the following, a case where the coding rate is 1/2 will be described as an example.

Formulas (3-1) to (3-3) are considered as parity check polynomials for LDPC-CC with a time-varying period of 3. At this time, X (D) is a polynomial expression of data (information), and P (D) is a polynomial expression of parity. Here, in the equations (3-1) to (3-3), it is assumed that the parity check polynomial has three terms in each of X (D) and P (D).

In Expression (3-1), a1, a2, and a3 are integers (where a1 ≠ a2 ≠ a3). B1, b2, and b3 are integers (where b1 ≠ b2 ≠ b3). The parity check polynomial of equation (3-1) is referred to as “check equation # 1”, and the sub-matrix based on the parity check polynomial of equation (3-1) is referred to as a first sub-matrix H ₁ .

In the formula (3-2), A1, A2, and A3 are integers (where A1 ≠ A2 ≠ A3). B1, B2, and B3 are integers (B1 ≠ B2 ≠ B3). Referred to parity check polynomial of equation (3-2) and "check equation # 2", the sub-matrix based on a parity check polynomial of equation (3-2), the second sub-matrix H _2.

In Expression (3-3), α1, α2, and α3 are integers (where α1 ≠ α2 ≠ α3). Β1, β2, and β3 are integers (where β1 ≠ β2 ≠ β3). The parity check polynomial of equation (3-3) is called “check equation # 3”, and the sub-matrix based on the parity check polynomial of equation (3-3) is referred to as a third sub-matrix H ₃ .

Then, consider LDPC-CC with a time varying period of 3 generated from the first sub-matrix H ₁ , second sub-matrix H ₂ , and third sub-matrix H ₃ .

  At this time, in the formulas (3-1) to (3-3), combinations of orders of X (D) and P (D) (a1, a2, a3), (b1, b2, b3), (A1, A2) , A3), (B1, B2, B3), (α1, α2, α3), (β1, β2, β3) divided by 3, and the remainder is k, the three expressed as above The coefficient set (for example, (a1, a2, a3)) includes the remainders 0, 1, and 2 and is satisfied with all the above three coefficient sets.

  For example, if the orders (a1, a2, a3) of X (D) of “inspection formula # 1” are (a1, a2, a3) = (6, 5, 4), the orders (a1, a2, a3) ) Divided by 3, the remainder k is (0, 2, 1), and the remainder (k) 0, 1, 2 is included in each of the three coefficient sets. Similarly, if the orders (b1, b2, b3) of P (D) of “inspection formula # 1” are (b1, b2, b3) = (3, 2, 1), the orders (b1, b2, The remainder k obtained by dividing b3) by 4 is (0, 2, 1), and the three coefficient sets include one each of 0, 1, and 2 as the remainder (k). It is assumed that the above “remainder” condition is also satisfied for each of the three coefficient sets of X (D) and P (D) of “inspection formula # 2” and “inspection formula # 3”.

  By generating LDPC-CC in this way, it is possible to generate a regular LDPC-CC code with equal row weights and equal column weights in all rows, with some exceptions. it can. Note that the exception means that the row weight and the column weight are not equal to other row weights and column weights in the first part and the last part of the parity check matrix. Further, when BP decoding is performed, the reliability in “check equation # 2” and the reliability in “check equation # 3” are accurately propagated to “check equation # 1”, and “check equation # 1”. And the reliability in “inspection equation # 3” are accurately propagated to “inspection equation # 2”, and the reliability in “inspection equation # 1” and the reliability in “inspection equation # 2” are Properly propagates to “inspection formula # 3”. For this reason, LDPC-CC with better reception quality can be obtained. This is because, when considered in units of columns, the positions where “1” exists are arranged so as to accurately propagate the reliability as described above.

  Hereinafter, the above-described reliability propagation will be described with reference to the drawings. FIG. 4A shows the configuration of a parity check polynomial and a check matrix H of an LDPC-CC with a time-varying period 3.

  “Check expression # 1” is the parity check polynomial of Expression (3-1), in which (a1, a2, a3) = (2,1,0), (b1, b2, b3) = (2,1,0) ) And the remainder obtained by dividing each coefficient by 3 is (a1% 3, a2% 3, a3% 3) = (2,1,0), (b1% 3, b2% 3, b3% 3) ) = (2, 1, 0). “Z% 3” represents the remainder of Z divided by 3 (the same applies hereinafter).

  “Check expression # 2” is the parity check polynomial of Expression (3-2), in which (A1, A2, A3) = (5, 1, 0), (B1, B2, B3) = (5, 1, 0) ), And the remainder of dividing each coefficient by 3 is (A1% 3, A2% 3, A3% 3) = (2,1,0), (B1% 3, B2% 3, B3% 3) ) = (2, 1, 0).

  “Check expression # 3” is obtained by using (α1, α2, α3) = (4, 2, 0), (β1, β2, β3) = (4, 2, 0) in the parity check polynomial of Expression (3-3). ), And the remainder of dividing each coefficient by 3 is (α1% 3, α2% 3, α3% 3) = (1,2,0), (β1% 3, β2% 3, β3% 3 ) = (1, 2, 0).

Therefore, the example of the LDPC-CC with the time varying period 3 shown in FIG. 4A is the above-described condition regarding the “remainder”, that is,
(A1% 3, a2% 3, a3% 3),
(B1% 3, b2% 3, b3% 3),
(A1% 3, A2% 3, A3% 3),
(B1% 3, B2% 3, B3% 3),
(Α1% 3, α2% 3, α3% 3),
(Β1% 3, β2% 3, β3% 3)
Any one of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) It satisfies the condition of becoming.

  Returning to FIG. 4A again, reliability propagation will be described. By the column operation of the column 6506 in the BP decoding, “1” in the region 6501 of “check equation # 1” is changed to “1” in region 6504 of “check matrix # 2” and “1” in region 6505 of “check matrix # 3”. The reliability is propagated from “1”. As described above, “1” in the area 6501 of the “check equation # 1” is a coefficient with which the remainder obtained by dividing by 3 is 0 (a3% 3 = 0 (a3 = 0) or b3% 3 = 0 (b3 = 0)). In addition, “1” in the area 6504 of “check matrix # 2” is a coefficient with a remainder obtained by dividing by 3 (A2% 3 = 1 (A2 = 1) or B2% 3 = 1 (B2 = 1)). In addition, “1” in the area 6505 of “inspection formula # 3” is a coefficient with a remainder obtained by dividing by 3 (α2% 3 = 2 (α2 = 2) or β2% 3 = 2 (β2 = 2)).

  As described above, “1” in the region 6501 in which the remainder of the coefficient of “check expression # 1” is 0 is 1 in the coefficient of “check expression # 2” in the column calculation of the column 6506 in BP decoding. Reliability is propagated from “1” in region 6504 and “1” in region 6505 in which the remainder is 2 in the coefficient of “check expression # 3”.

  Similarly, “1” in the region 6502 in which the remainder is 1 in the coefficient of “check equation # 1” is a region in which the remainder is 2 in the coefficient of “check equation # 2” in the column calculation of the column 6509 in BP decoding. The reliability is propagated from “1” of 6507 “1” and “1” of the region 6508 in which the remainder is 0 in the coefficient of “checking formula # 3”.

  Similarly, “1” in the region 6503 in which the remainder is 2 in the coefficient of “check equation # 1” is a region in which the remainder is 0 in the coefficient of “check equation # 2” in the column calculation of the column 6512 in BP decoding. The reliability is propagated from “1” of 6510 “1” and “1” of the region 6511 in which the remainder is 1 in the coefficient of “check equation # 3”.

  A supplementary explanation of reliability propagation will be given with reference to FIG. 4B. FIG. 4B shows the relationship of reliability propagation between the terms relating to X (D) of “check equation # 1” to “check equation # 3” in FIG. 4A. “Checking Formula # 1” to “Checking Formula # 3” in FIG. 4A are expressed in terms of X (D) in Formulas (3-1) to (3-3) as follows: (a1, a2, a3) = (2, 1, 0), (A1, A2, A3) = (5, 1, 0), (α1, α2, α3) = (4, 2, 0).

  In FIG. 4B, the terms (a3, A3, α3) enclosed by the squares indicate coefficients with a remainder of 0 divided by 3. Further, the terms (a2, A2, α1) surrounded by circles indicate a coefficient whose remainder is 1 after dividing by 3. In addition, the terms (a1, A1, α2) surrounded by rhombuses indicate coefficients with a remainder of 2 divided by 3.

  As can be seen from FIG. 4B, the reliability of a1 of “check equation # 1” is propagated from A3 of “check equation # 2” and α1 of “check equation # 3”, which have different remainders after division by 3. The reliability of “a2” of “check equation # 1” is propagated from A1 of “check equation # 2” and α3 of “check equation # 3”, which have different remainders after division by 3. The reliability of “a3” of “checking formula # 1” is propagated from A2 of “checking formula # 2” and α2 of “checking formula # 3”, which have different remainders divided by 3. FIG. 4B shows the relationship of reliability propagation between the terms related to X (D) of “checking formula # 1” to “checking formula # 3”, but the same applies to the terms related to P (D). I can say that.

  As described above, the reliability is propagated to the “check equation # 1” from the coefficients of which the remainder obtained by dividing by 3 is 0, 1, 2 among the coefficients of the “check equation # 2”. That is, the reliability is propagated to the “checking formula # 1” from the coefficients of the “checking formula # 2” that are all different in the remainder after division by 3. Therefore, all the reliability levels with low correlation are propagated to “check formula # 1”.

  Similarly, the reliability is propagated to the “check formula # 2” from the coefficients of which the remainder obtained by dividing by 3 among the coefficients of the “check formula # 1” is 0, 1 and 2. That is, the reliability is propagated to the “check equation # 2” from the coefficients of the “check equation # 1”, all of which have different remainders after division by 3. Also, the reliability is propagated to “check formula # 2” from the coefficients of which the remainder obtained by dividing by 3 is 0, 1, and 2 among the coefficients of “check formula # 3”. That is, the reliability is propagated to the “check equation # 2” from the coefficients of the “check equation # 3”, all of which have different remainders after division by 3.

  Similarly, the reliability is propagated to “check formula # 3” from the coefficients of “check formula # 1” whose remainders after division by 3 are 0, 1, and 2. That is, the reliability is propagated to the “check equation # 3” from the coefficients of the “check equation # 1”, all of which have different remainders after division by 3. Also, the reliability is propagated to “check formula # 3” from the coefficients of which the remainder obtained by dividing by 3 becomes 0, 1 and 2 among the coefficients of “check formula # 2”. That is, the reliability is propagated to the “checking formula # 3” from the coefficients of the “checking formula # 2”, all of which have different remainders after division by 3.

  As described above, by ensuring that the respective orders of the parity check polynomials of the expressions (3-1) to (3-3) satisfy the above-mentioned condition regarding “remainder”, the reliability is always ensured in all column operations. Since it is propagated, the reliability can be propagated efficiently in all the check equations, and the error correction capability can be further increased.

  As described above, the LDPC-CC with the time varying period 3 has been described by taking the case of the coding rate 1/2 as an example, but the coding rate is not limited to 1/2. In the case of coding rate (n-1) / n (n is an integer of 2 or more), each of the three coefficients in information X1 (D), X2 (D),... Xn-1 (D) If the condition regarding the “remainder” is satisfied in the set, it becomes a regular LDPC code, and good reception quality can be obtained.

  Hereinafter, the case of coding rate (n−1) / n (n is an integer of 2 or more) will be described.

Formulas (4-1) to (4-3) are considered as parity check polynomials for LDPC-CC with a time-varying period of 3. In this _{case, X 1 (D), X} 2 (D), ··· X n-1 (D) is data _{(information)} X _1, X 2, a polynomial representation of ··· _{X n-1,} P (D) is a polynomial expression of parity. Here, in the formulas (4-1) to (4-3), X ₁ (D), X ₂ (D),... X _n-1 (D), P (D) each have three terms. Let the parity check polynomial exist.

In the equation (4-1), a _{i, 1} , a _{i, 2} , a _{i, 3} (i = 1, 2,..., N−1) are integers (where a _{i, 1} ≠ a _{i, 2} ≠ a _{i, 3} ). B1, b2, and b3 are integers (where b1 ≠ b2 ≠ b3). The parity check polynomial of equation (4-1) is referred to as “check equation # 1”, and the sub-matrix based on the parity check polynomial of equation (4-1) is defined as a first sub-matrix H ₁ .

In the equation (4-2), A _{i, 1} , A _{i, 2} , A _{i, 3} (i = 1, 2,..., N−1 are integers (where A _{i, 1} ≠ A _{i , 2} ≠ A _{i, 3} ) and B1, B2, and B3 are integers (where B1 ≠ B2 ≠ B3), and the parity check polynomial of equation (4-2) is “check equation # 2”. call, the sub-matrix based on a parity check polynomial of equation (4-2), the second sub-matrix _{H 2.}

In formula (4-3), α _{i, 1} , α _{i, 2} , α _{i, 3} (where i = 1, 2,..., N−1 is an integer (where α _{i, 1} ≠ α _{i , 2} ≠ α _{i, 3} ) and β1, β2, and β3 are integers (where β1 ≠ β2 ≠ β3), and the parity check polynomial of equation (4-3) is “check equation # 3”. A sub-matrix based on the parity check polynomial of Equation (4-3) is referred to as a third sub-matrix H ₃ .

Then, consider LDPC-CC with a time varying period of 3 generated from the first sub-matrix H ₁ , second sub-matrix H ₂ , and third sub-matrix H ₃ .

At this time, in the formulas (4-1) to (4-3), combinations of orders of X ₁ (D), X ₂ (D),... X _n-1 (D) and P (D) (a _{1,1, a 1,2, a 1,3)} ,
(A _2,1 , a _2,2 , a _2,3 ), ...,
(A _n-1,1 , a _n-1,2 , a _n-1,3 ),
(B1, b2, b3),
(A _1,1 , A _1,2 , A _1,3 ),
(A _2,1 , A _2,2 , A _2,3 ), ...
(A _n-1,1 , A _n-1,2 , A _n-1,3 ),
(B1, B2, B3),
(Α _1,1 , α _1,2 , α _1,3 ),
(Α _2,1 , α _2,2 , α _2,3 ), ...
(Α _n-1,1 , α _n-1,2 , α _n-1,3 ),
(Β1, β2, β3)
When the remainder obtained by dividing each value of n by 3 is k, the three coefficient sets expressed as described above (for example, (a _1,1 , a ₁ , ₂ , a _1,3 )) have a remainder of 0, 1 and 2 are included one by one, and all three coefficient sets are satisfied.

That means
(A _1,1 % 3, a _1,2 % 3, a _1,3 % 3),
(A _2,1 % 3, a _2,2 % 3, a _2,3 % 3), ...
( _An-1,1 % 3, _{ann -1,2} % 3, _ann-1,3 % 3),
(B1% 3, b2% 3, b3% 3),
(A _1,1 % 3, A _1,2 % 3, A _1,3 % 3),
(A _2,1 % 3, A _2,2 % 3, A _2,3 % 3), ...
(A _n-1,1 % 3, A _n-1,2 % 3, A _n-1,3 % 3),
(B1% 3, B2% 3, B3% 3),
(Α _1,1 % 3, α _1,2 % 3, α _1,3 % 3),
(Α _2,1 % 3, α _2,2 % 3, α _2,3 % 3), ...,
(Α _n-1,1 % 3, α _n-1,2 % 3, α _n-1,3 % 3),
(Β1% 3, β2% 3, β3% 3)
Any one of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) To be.

  By generating LDPC-CC in this way, a regular LDPC-CC code can be generated. Further, when BP decoding is performed, the reliability in “check equation # 2” and the reliability in “check equation # 3” are accurately propagated to “check equation # 1”, and “check equation # 1”. And the reliability in “inspection equation # 3” are accurately propagated to “inspection equation # 2”, and the reliability in “inspection equation # 1” and the reliability in “inspection equation # 2” are Properly propagates to “inspection formula # 3”. For this reason, LDPC-CC with better reception quality can be obtained as in the case of the coding rate of 1/2.

Table 3 shows an example of LDPC-CC (LDPC-CC # 1, # 2, # 3, # 4, # 5) having a time-varying period of 3 and a coding rate of ½, in which the condition regarding the “remainder” is satisfied. ). In Table 3, the LDPC-CC with time-varying period 3 is represented by three parity check polynomials of “check (multinomial) equation # 1”, “check (multinomial) equation # 2”, and “check (multinomial) equation # 3”. Defined.

  Similarly to the time-varying period 3, the following conditions regarding “remainder” are applied to LDPC-CC whose time-varying period is a multiple of 3 (for example, the time-varying period is 6, 9, 12,...). Then, it was confirmed that a code with good characteristics can be searched. Hereinafter, the LDPC-CC having a multiple of the time-varying period 3 with good characteristics will be described. In the following, a case of LDPC-CC with a coding rate of 1/2 and a time varying period of 6 will be described as an example.

Formulas (5-1) to (5-6) are considered as LDPC-CC parity check polynomials with a time-varying period of 6.

At this time, X (D) is a polynomial expression of data (information), and P (D) is a polynomial expression of parity. In LDPC-CC with time varying period 6, parity i and information Xi at time i are assumed to be i% 6 = k (k = 0, 1, 2, 3, 4, 5), equation (5- (k + 1)) ) Parity check polynomial. For example, if i = 1, i% 6 = 1 (k = 1), and therefore Equation (6) is established.

  Here, in equations (5-1) to (5-6), it is assumed that the parity check polynomial is such that three terms exist in each of X (D) and P (D).

In Expression (5-1), a1,1, a1,2, and a1,3 are integers (where a1,1 ≠ a1,2 ≠ a1,3). Further, b1,1, b1,2, b1,3 are integers (where b1,1 ≠ b1,2 ≠ b1,3). The parity check polynomial of equation (5-1) is referred to as “check equation # 1”, and a sub-matrix based on the parity check polynomial of equation (5-1) is defined as a first sub-matrix H ₁ .

In equation (5-2), a2, 1, a2, 2, a2, 3 are integers (where a2, 1 ≠ a2, 2 ≠ a2, 3). In addition, b2,1, b2,2, b2,3 are integers (where b2,1 ≠ b2,2 ≠ b2,3). Referred to parity check polynomial of equation (5-2) and "check equation # 2", the sub-matrix based on a parity check polynomial of equation (5-2), the second sub-matrix H _2.

In Expression (5-3), a3, 1, a3, 2, and a3, 3 are integers (where a3, 1 ≠ a3, 2 ≠ a3, 3). B3, 1, b3, 2, b3, 3 are integers (where b3, 1 ≠ b3, 2 ≠ b3, 3). The parity check polynomial of equation (5-3) is referred to as “check equation # 3”, and a sub-matrix based on the parity check polynomial of equation (5-3) is referred to as a third sub-matrix H ₃ .

In the formula (5-4), a4, 1, a4, 2, and a4, 3 are integers (where a4, 1 ≠ a4, 2 ≠ a4, 3). Also, b4, 1, b4, 2, b4, 3 are integers (where b4, 1 ≠ b4, 2 ≠ b4, 3). The parity check polynomial of equation (5-4) is referred to as “check equation # 4”, and the sub-matrix based on the parity check polynomial of equation (5-4) is referred to as a fourth sub-matrix H ₄ .

In Expression (5-5), a5, 1, a5, 2, and a5, 3 are integers (where a5, 1 ≠ a5, 2 ≠ a5, 3). Also, b5, 1, b5, 2, and b5, 3 are integers (where b5, 1 ≠ b5, 2 ≠ b5, 3). Referred to parity check polynomial of equation (5-5) and "check equation # 5", a sub-matrix based on a parity check polynomial of equation (5-5), the fifth sub-matrix H _5.

In the formula (5-6), a6, 1, a6, 2, a6, 3 are integers (where a6, 1 ≠ a6, 2 ≠ a6, 3). B6, 1, b6, 2, b6, 3 are integers (where b6, 1 ≠ b6, 2 ≠ b6, 3). The parity check polynomial of equation (5-6) is referred to as “check equation # 6”, and the sub-matrix based on the parity check polynomial of equation (5-6) is referred to as a sixth sub-matrix H ₆ .

The first sub-matrix _{H 1,} second sub-matrix _{H 2,} third sub-matrix _{H 3,} fourth sub-matrix _{H 4,} fifth sub-matrix _{H 5,} varying period 6 when generating the sixth sub-matrix _{H 6} Think about LDPC-CC.

At this time, in formulas (5-1) to (5-6), combinations of orders of X (D) and P (D) (a1, 1, a1, 2, a1, 3),
(B1,1, b1,2, b1,3),
(A2,1, a2,2, a2,3),
(B2,1, b2,2, b2,3),
(A3, 1, a3, 2, a3, 3),
(B3, 1, b3, 2, b3, 3),
(A4, 1, a4, 2, a4, 3),
(B4, 1, b4, 2, b4, 3),
(A5, 1, a5, 2, a5, 3),
(B5, 1, b5, 2, b5, 3),
(A6, 1, a6, 2, a6, 3),
(B6, 1, b6, 2, b6, 3)
When the remainder k is divided by 3, the remainder is k, and the three coefficient sets expressed as described above (for example, (a1, 1, a1, 2, a1, 3)) have a remainder of 0, 1, 1, 2 are included one by one, and all the above three coefficient sets are satisfied. That means
(A1, 1% 3, a1,2% 3, a1,3% 3),
(B1, 1% 3, b1, 2% 3, b1, 3% 3),
(A2, 1% 3, a2, 2% 3, a2, 3% 3),
(B2, 1% 3, b2, 2% 3, b2, 3% 3),
(A3, 1% 3, a3, 2% 3, a3, 3% 3),
(B3, 1% 3, b3, 2% 3, b3, 3% 3),
(A4, 1% 3, a4, 2% 3, a4, 3% 3),
(B4, 1% 3, b4, 2% 3, b4, 3% 3),
(A5, 1% 3, a5, 2% 3, a5, 3% 3),
(B5, 1% 3, b5, 2% 3, b5, 3% 3),
(A6, 1% 3, a6, 2% 3, a6, 3% 3),
(B6, 1% 3, b6, 2% 3, b6, 3% 3)
Any one of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become.

  By generating LDPC-CC in this way, when a Tanner graph is drawn with respect to “inspection formula # 1”, if there is an edge, “examination formula # 2 or inspection formula # 5 ”And the reliability in“ Checking Formula # 3 or Checking Formula # 6 ”are accurately propagated.

  Further, when an edge is present when a Tanner graph is drawn with respect to “inspection formula # 2”, the reliability in “inspection formula # 1 or inspection formula # 4” is accurately determined, “inspection formula # 3, Or, the reliability in the inspection formula # 6 ”is accurately propagated.

  In addition, when an edge is present when a Tanner graph is drawn for “inspection equation # 3”, the reliability in “inspection equation # 1 or inspection equation # 4” is accurately determined, “inspection equation # 2, Or, the reliability in the inspection formula # 5 ”is accurately transmitted. When the Tanner graph is drawn for “inspection formula # 4”, if there is an edge, the reliability in “inspection formula # 2 or inspection formula # 5”, “inspection formula # 3, or The reliability in the inspection formula # 6 "is accurately transmitted.

  In addition, when an edge is present when the Tanner graph is drawn, the reliability in “inspection formula # 1 or inspection formula # 4” is accurately compared with “inspection formula # 3”. Or, the reliability in the inspection formula # 6 ”is accurately propagated. In addition, when an edge is present when a Tanner graph is drawn for “inspection formula # 6”, the reliability in “inspection formula # 1 or inspection formula # 4” is accurately determined, “inspection formula # 2, Or, the reliability in the inspection formula # 5 ”is accurately transmitted.

  For this reason, as in the case where the time varying period is 3, the LDPC-CC having the time varying period 6 retains better error correction capability.

  About this, reliability propagation is demonstrated using FIG. 4C. FIG. 4C shows the relationship of reliability propagation between the terms relating to X (D) of “check equation # 1” to “check equation # 6”. In FIG. 4C, a square indicates a coefficient with a remainder of 0 divided by 3 in ax, y (x = 1, 2, 3, 4, 5, 6; y = 1, 2, 3).

  In addition, the circles indicate coefficients with a remainder of 1 after dividing by 3 in ax, y (x = 1, 2, 3, 4, 5, 6; y = 1, 2, 3). The rhombus indicates a coefficient with a remainder of 2 obtained by dividing 3 in ax, y (x = 1, 2, 3, 4, 5, 6; y = 1, 2, 3).

  As can be seen from FIG. 4C, when the Tanner graph is drawn, if there is an edge, a1,1 of “inspection equation # 1” is different from “inspection equation # 2 or # 5” and “ The reliability is propagated from the inspection formula # 3 or # 6 ". Similarly, when the Tanner graph is drawn, if there is an edge, a1 and a2 of “inspection formula # 1” are different from each other in “inspection formula # 2 or # 5” and “inspection formula # 3”. Or, the reliability is propagated from # 6 ".

  Similarly, when a Tanner graph is drawn, if there is an edge, a1,3 of “inspection formula # 1” are different from “inspection formula # 2 or # 5” and “inspection formula # 3” with different remainders divided by 3 Or, the reliability is propagated from # 6 ". FIG. 4C shows the reliability propagation relationship between the terms related to X (D) of “checking formula # 1” to “checking formula # 6”, but the same applies to the terms related to P (D). I can say that.

  As described above, the reliability is propagated to each node in the Tanner graph of “check formula # 1” from the coefficient nodes other than “check formula # 1”. Therefore, all of the reliability levels having low correlation are propagated to “checking formula # 1”, which is considered to improve the error correction capability.

  In FIG. 4C, attention is paid to “inspection formula # 1”, but a “tanner graph” can be similarly drawn for “inspection formula # 2” to “inspection formula # 6”. The reliability is propagated to each node from coefficient nodes other than “check expression #K”. Accordingly, all of the reliability levels having low correlation are propagated to “checking formula #K”, so that it is considered that the error correction capability is improved. (K = 2, 3, 4, 5, 6)

  In this way, by making the respective orders of the parity check polynomials of the equations (5-1) to (5-6) satisfy the condition regarding the “remainder” described above, the reliability can be efficiently obtained in all the check equations. Can be propagated, and the possibility that the error correction capability can be further increased is increased.

As described above, the LDPC-CC with the time varying period 6 has been described by taking the case of the coding rate 1/2 as an example, but the coding rate is not limited to 1/2. In the case of coding rate (n-1) / n (n is an integer of 2 or more), each of information X ₁ (D), X ₂ (D), ... X _n-1 (D) If the condition regarding the “remainder” is satisfied in the three coefficient sets, the possibility of obtaining good reception quality is increased.

  Hereinafter, the case of coding rate (n−1) / n (n is an integer of 2 or more) will be described.

Equations (7-1) to (7-6) are considered as parity check polynomials for LDPC-CC with a time-varying period of 6.

At this time, X ₁ (D), X ₂ (D),... X _n−1 (D) is a polynomial expression of data (information) X 1, X 2,. Is a polynomial representation of parity. Here, in the formulas (7-1) to (7-6), X ₁ (D), X ₂ (D),... X _n-1 (D), P (D) each have three terms. Let the parity check polynomial exist. When the coding rate is ½ and when considered in the same manner as the time-varying period 3, the time-varying period 6, code represented by the parity check polynomials of equations (7-1) to (7-6) In an LDPC-CC with a conversion rate (n-1) / n (n is an integer of 2 or more), if the following condition (<condition # 1>) is satisfied, there is a possibility that higher error correction capability can be obtained. Rise.

However, in an LDPC-CC having a time varying period of 6 and a coding rate (n−1) / n (n is an integer of 2 or more), the parity at time i is Pi and the information is X _{i, 1} , X _{i, 2} , ..., represented by Xi _{, n-1} . At this time, if i% 6 = k (k = 0, 1, 2, 3, 4, 5), the parity check polynomial of Expression (7- (k + 1)) is established. For example, if i = 8, i% 6 = 2 (k = 2), and therefore equation (8) is established.

<Condition # 1>
In the formulas (7-1) to (7-6), the combination of the orders of X ₁ (D), X ₂ (D),... X _n-1 (D) and P (D) satisfies the following conditions. Fulfill.
(A _{# 1,1,1} % 3, a _{# 1,1,2} % 3, a _{# 1,1,3} % 3),
(A _{# 1,2,1} % 3, a _{# 1,2,2} % 3, a _{# 1,2,3} % 3), ...
(A _{# 1, k, 1} % 3, a _{# 1, k, 2} % 3, a _{# 1, k, 3} % 3), ...
(A _{# 1, n-1,1} % 3, a _{# 1, n-1,2} % 3, a _{# 1, n-1,3} % 3),
(B _{# 1,1} % 3, b _{# 1,2} % 3, b _{# 1,3} % 3)
Any one of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become. (K = 1, 2, 3,..., N-1)
And,
_{(A # 2,1,1% 3, a} # 2,1,2% 3, a # 2,1,3% 3),
(A _{# 2,2,1} % 3, a _{# 2,2,2} % 3, a _{# 2,2,3} % 3), ...
(A _{# 2, k, 1} % 3, a _{# 2, k, 2} % 3, a _{# 2, k, 3} % 3), ...
(A _{# 2, n-1,1} % 3, a _{# 2, n-1,2} % 3, a _{# 2, n-1,3} % 3),
(B _{# 2,1} % 3, b _{# 2,2} % 3, b _{# 2,3} % 3)
Any one of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become. (K = 1, 2, 3,..., N-1)
And,
_{(A # 3,1,1% 3, a} # 3,1,2% 3, a # 3,1,3% 3),
(A _{# 3,2,1} % 3, a _{# 3,2,2} % 3, a _{# 3,2,3} % 3), ...
(A _{# 3, k, 1} % 3, a _{# 3, k, 2} % 3, a _{# 3, k, 3} % 3), ...,
(A _{# 3, n-1, 1} % 3, a _{# 3, n-1, 2} % 3, a _{# 3, n-1, 3} % 3),
(B _{# 3, 1} % 3, b _{# 3, 2} % 3, b _{# 3, 3} % 3)
Any one of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become. (K = 1, 2, 3,..., N-1)
And,
(A _{# 4,1,1} % 3, a _{# 4,1,2} % 3, a _{# 4,1,3} % 3),
_{(A # 4,2,1% 3, a} # 4,2,2% 3, a # 4,2,3% 3), ···,
(A _{# 4, k, 1} % 3, a _{# 4, k, 2} % 3, a _{# 4, k, 3} % 3), ...
(A _{# 4, n-1, 1} % 3, a _{# 4, n-1, 2} % 3, a _{# 4, n-1, 3} % 3),
(B _{# 4,1} % 3, b _{# 4,2} % 3, b _{# 4,3} % 3)
Any one of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become. (K = 1, 2, 3,..., N-1)
And,
(A _{# 5,1,1} % 3, a _{# 5,1,2} % 3, a _{# 5,1,3} % 3),
(A _{# 5,} 2, 1% 3, a _{# 5, 2, 2} % 3, a _{# 5, 2,} 3% 3), ...
(A _{# 5, k, 1} % 3, a _{# 5, k, 2} % 3, a _{# 5, k, 3} % 3), ...
(A _{# 5, n-1, 1} % 3, a _{# 5, n-1, 2} % 3, a _{# 5, n-1, 3} % 3),
(B _{# 5, 1} % 3, b _{# 5, 2} % 3, b _{# 5, 3} % 3)
Any one of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become. (K = 1, 2, 3,..., N-1)
And,
(A _{# 6,1,1} % 3, a _{# 6,1,2} % 3, a _{# 6,1,3} % 3),
(A _{# 6,2,1} % 3, a _{# 6,2,2} % 3, a _{# 6,2,3} % 3), ...
(A _{# 6, k, 1} % 3, a _{# 6, k, 2} % 3, a _{# 6, k, 3} % 3), ...
(A _{# 6, n-1, 1} % 3, a _{# 6, n-1, 2} % 3, a _{# 6, n-1, 3} % 3),
(B _{# 6, 1} % 3, b _{# 6, 2} % 3, b _{# 6, 3} % 3)
Any one of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become. (K = 1, 2, 3,..., N-1)

  In the above description, a code having a high error correction capability in the LDPC-CC with the time varying period 6 has been described. However, as with the LDPC-CC design method with the time varying periods 3 and 6, the time varying period 3g (g = 1). 2, 3, 4,...) LDPC-CC (that is, LDPC-CC whose time-varying period is a multiple of 3), a code having high error correction capability can be generated. Hereinafter, a method for configuring the code will be described in detail.

An LDPC-CC parity check polynomial with a time-varying period of 3 g (g = 1, 2, 3, 4,...) And coding rate (n−1) / n (n is an integer of 2 or more) Consider (9-1) to (9-3g).

In this _{case, X 1 (D), X} 2 (D), ··· X n-1 (D) is data _{(information)} X _1, X 2, a polynomial representation of ··· _{X n-1,} P (D) is a polynomial expression of parity. Here, in the formulas (9-1) to (9-3g), X ₁ (D), X ₂ (D),... X _n-1 (D), P (D) each have three terms. Let the parity check polynomial exist.

  When considered in the same manner as the LDPC-CC with the time varying period 3 and the LDPC-CC with the time varying period 6, the time varying period 3g represented by the parity check polynomials of the equations (9-1) to (9-3g), the coding rate In the LDPC-CC of (n-1) / n (n is an integer of 2 or more), when the following condition (<condition # 2>) is satisfied, the possibility that higher error correction capability can be obtained increases.

However, in an LDPC-CC with a time varying period of 3 g and a coding rate (n−1) / n (n is an integer of 2 or more), the parity at time i is Pi and the information is X _{i, 1} , X _{i, 2} , ..., represented by Xi _{, n-1} . At this time, if i% 3g = k (k = 0, 1, 2,..., 3g−1), the parity check polynomial of Expression (9− (k + 1)) is established. For example, if i = 2, i% 3g = 2 (k = 2), and therefore equation (10) is established.

In addition, in the formulas (9-1) to (9-3g), a _{# k, p, 1} , a _{# k, p, 2} , a _{# k, p, 3} are integers (however, a _{# k, p , 1} ≠ a _{#k, p, 2} ≠ a _{#k, p, 3} ) (k = 1, 2, 3,..., 3g: p = 1, 2, 3,..., N− 1). Also, b _{# k, 1} , b _{# k, 2} , and b _{# k, 3} are integers (where b _{# k, 1} ≠ b _{# k, 2} ≠ b _{# k, 3} ). The parity check polynomial (k = 1, 2, 3,..., 3g) in Expression (9-k) is called “check expression #k”, and a sub-matrix based on the parity check polynomial in Expression (9-k) is K-th sub-matrix H _k . The first sub-matrix _{H 1,} second sub-matrix _{H 2,} third sub-matrix _H 3, considered ..., for LDPC-CC of varying period 3g when producing from a 3g submatrix _{H 3g.}

<Condition # 2>
In the formulas (9-1) to (9-3g), the combination of the orders of X ₁ (D), X ₂ (D),... X _n-1 (D) and P (D) satisfies the following conditions. Fulfill.
(A _{# 1,1,1} % 3, a _{# 1,1,2} % 3, a _{# 1,1,3} % 3),
(A _{# 1,2,1} % 3, a _{# 1,2,2} % 3, a _{# 1,2,3} % 3), ...
(A _{# 1, p, 1} % 3, a _{# 1, p, 2} % 3, a _{# 1, p, 3} % 3), ...
(A _{# 1, n-1,1} % 3, a _{# 1, n-1,2} % 3, a _{# 1, n-1,3} % 3),
(B _{# 1,1} % 3, b _{# 1,2} % 3, b _{# 1,3} % 3)
Any one of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become. (P = 1, 2, 3,..., N-1)
And,
_{(A # 2,1,1% 3, a} # 2,1,2% 3, a # 2,1,3% 3),
(A _{# 2,2,1} % 3, a _{# 2,2,2} % 3, a _{# 2,2,3} % 3), ...
(A _{# 2, p, 1} % 3, a _{# 2, p, 2} % 3, a _{# 2, p, 3} % 3), ...
(A _{# 2, n-1,1} % 3, a _{# 2, n-1,2} % 3, a _{# 2, n-1,3} % 3),
(B _{# 2,1} % 3, b _{# 2,2} % 3, b _{# 2,3} % 3)
Any one of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become. (P = 1, 2, 3,..., N-1)
And,
_{(A # 3,1,1% 3, a} # 3,1,2% 3, a # 3,1,3% 3),
(A _{# 3,2,1} % 3, a _{# 3,2,2} % 3, a _{# 3,2,3} % 3), ...
(A _{# 3, p, 1} % 3, a _{# 3, p, 2} % 3, a _{# 3, p, 3} % 3), ...
(A _{# 3, n-1, 1} % 3, a _{# 3, n-1, 2} % 3, a _{# 3, n-1, 3} % 3),
(B _{# 3, 1} % 3, b _{# 3, 2} % 3, b _{# 3, 3} % 3)
Any one of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become. (P = 1, 2, 3,..., N-1)
And,
・
・
・
And,
(A _{# k, 1,1} % 3, a _{# k, 1,2} % 3, a _{# k, 1,3} % 3),
(A _{# k, 2,1} % 3, a _{# k, 2,2} % 3, a _{# k, 2,3} % 3), ...
(A _{# k, p, 1} % 3, a _{# k, p, 2} % 3, a _{# k, p, 3} % 3), ...,
(A _{# k, n-1,1} % 3, a _{# k, n-1,2} % 3, a _{# k, n-1,3} % 3),
(B _{# k, 1} % 3, b _{# k, 2} % 3, b _{# k, 3} % 3)
Any one of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become. (P = 1, 2, 3,..., N-1) (hence, k = 1, 2, 3,..., 3g)
And,
・
・
・
And,
_{(A # 3g-2,1,1% 3} , a # 3g-2,1,2% 3, a # 3g-2,1,3% 3),
(A _{# 3g-2,2,1} % 3, a _{# 3g-2,2,2} % 3, a _{# 3g-2,2,3} % 3), ...
(A _{# 3g-2, p, 1} % 3, a _{# 3g-2, p, 2} % 3, a _{# 3g-2, p, 3} % 3), ...
(A _{# 3g-2, n-1,1} % 3, a _{# 3g-2, n-1,2} % 3, a _{# 3g-2, n-1,3} % 3),
(B _{# 3g-2,1} % 3, b _{# 3g-2,2} % 3, b _{# 3g-2,3} % 3)
Any one of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become. (P = 1, 2, 3,..., N-1)
And,
(A _{# 3g-1,1,1} % 3, a _{# 3g-1,1,2} % 3, a _{# 3g-1,1,3} % 3),
(A _{# 3g-1,2,1} % 3, a _{# 3g-1,2,2} % 3, a _{# 3g-1,2,3} % 3), ...,
(A _{# 3g-1, p, 1} % 3, a _{# 3g-1, p, 2} % 3, a _{# 3g-1, p, 3} % 3), ...
(A _{# 3g-1, n-1,1} % 3, a _{# 3g-1, n-1,2} % 3, a _{# 3g-1, n-1,3} % 3),
(B _{# 3g-1,1} % 3, b _{# 3g-1,2} % 3, b _{# 3g-1,3} % 3)
Any one of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become. (P = 1, 2, 3,..., N-1)
And,
(A _{# 3g, 1,1} % 3, a _{# 3g, 1,2} % 3, a _{# 3g, 1,3} % 3),
(A _{# 3g, 2,1} % 3, a _{# 3g, 2,2} % 3, a _{# 3g, 2,3} % 3), ...
(A _{# 3g, p, 1} % 3, a _{# 3g, p, 2} % 3, a _{# 3g, p, 3} % 3), ...,
(A _{# 3g, n-1,1} % 3, a _{# 3g, n-1,2} % 3, a _{# 3g, n-1,3} % 3),
(B _{# 3g, 1} % 3, b _{# 3g, 2} % 3, b _{# 3g, 3} % 3)
Any one of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become. (P = 1, 2, 3,..., N-1)

However, in consideration of the fact that encoding is performed easily, in the equations (9-1) to (9-3g),
Of the three (b _{# k, 1} % 3, b _{# k, 2} % 3, b _{# k, 3} % 3), one “0” may be present (where k = 1, 2,... 3g). At this time, if D ⁰ = 1 exists and b _{# k, 1} , b _{# k, 2} , and b _{# k, 3} are integers of 0 or more, the parity P can be obtained sequentially. Because it has.

In addition, in order to correlate the parity bit and the data bit at the same time and easily search for a code having a high correction capability,
There is one “0” out of three (a _{# k, 1,1} % 3, a _{# k, 1,2} % 3, a _{# k, 1,3} % 3),
There is one “0” among the three (a _{# k, 2,1} % 3, a _{# k, 2,2} % 3, a _{# k, 2,3} % 3),
・
・
・
There is one “0” out of three (a _{# k, p, 1} % 3, a _{# k, p, 2} % 3, a _{# k, p, 3} % 3),
・
・
・
Of the three (a _{# k, n-1,1} % 3, a _{# k, n-1,2} % 3, a _{# k, n-1,3} % 3), there should be one "0". (However, k = 1, 2,... 3 g).

Next, consider an LDPC-CC with a time-varying period of 3 g (g = 2, 3, 4, 5,...) In consideration of easy encoding. At this time, assuming that the coding rate is (n-1) / n (n is an integer of 2 or more), the parity check polynomial of LDPC-CC can be expressed as follows.

In this _{case, X 1 (D), X} 2 (D), ··· X n-1 (D) is data _{(information)} X _1, X 2, a polynomial representation of ··· _{X n-1,} P (D) is a polynomial expression of parity. Here, in the formulas (11-1) to (11-3g), X ₁ (D), X ₂ (D),... X _n-1 (D), P (D) each have three terms. Let the parity check polynomial exist. However, in an LDPC-CC with a time varying period of 3 g and a coding rate (n−1) / n (n is an integer of 2 or more), the parity at time i is Pi and the information is X _{i, 1} , X _{i, 2} , ..., represented by Xi _{, n-1} . At this time, if i% 3g = k (k = 0, 1, 2,..., 3g−1), the parity check polynomial of Expression (11− (k + 1)) is established. For example, if i = 2, i% 3g = 2 (k = 2), and therefore equation (12) is established.

  At this time, if <Condition # 3> and <Condition # 4> are satisfied, the possibility that a code having higher error correction capability can be created increases.

<Condition # 3>
In the formulas (11-1) to (11-3g), the combinations of the orders of X1 (D), X2 (D),... Xn-1 (D) satisfy the following conditions.
(A _{# 1,1,1} % 3, a _{# 1,1,2} % 3, a _{# 1,1,3} % 3),
(A _{# 1,2,1} % 3, a _{# 1,2,2} % 3, a _{# 1,2,3} % 3), ...
(A _{# 1, p, 1} % 3, a _{# 1, p, 2} % 3, a _{# 1, p, 3} % 3), ...
(A _{# 1, n-1,1} % 3, a _{# 1, n-1,2} % 3, a _{# 1, n-1,3} % 3)
Any one of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become. (P = 1, 2, 3,..., N-1)
And,
_{(A # 2,1,1% 3, a} # 2,1,2% 3, a # 2,1,3% 3),
(A _{# 2,2,1} % 3, a _{# 2,2,2} % 3, a _{# 2,2,3} % 3), ...
(A _{# 2, p, 1} % 3, a _{# 2, p, 2} % 3, a _{# 2, p, 3} % 3), ...
(A _{# 2, n-1,1} % 3, a _{# 2, n-1,2} % 3, a _{# 2, n-1,3} % 3)
Any one of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become. (P = 1, 2, 3,..., N-1)
And,
_{(A # 3,1,1% 3, a} # 3,1,2% 3, a # 3,1,3% 3),
(A _{# 3,2,1} % 3, a _{# 3,2,2} % 3, a _{# 3,2,3} % 3), ...
(A _{# 3, p, 1} % 3, a _{# 3, p, 2} % 3, a _{# 3, p, 3} % 3), ...
(A _{# 3, n-1,1} % 3, a _{# 3, n-1,2} % 3, a _{# 3, n-1,3} % 3)
Any one of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become. (P = 1, 2, 3,..., N-1)
And,
・
・
・
And,
(A _{# k, 1,1} % 3, a _{# k, 1,2} % 3, a _{# k, 1,3} % 3),
(A _{# k, 2,1} % 3, a _{# k, 2,2} % 3, a _{# k, 2,3} % 3), ...
(A _{# k, p, 1} % 3, a _{# k, p, 2} % 3, a _{# k, p, 3} % 3), ...,
(A _{# k, n-1,1} % 3, a _{# k, n-1,2} % 3, a _{# k, n-1,3} % 3)
Any one of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become. (P = 1, 2, 3,..., N-1) (hence, k = 1, 2, 3,..., 3g)
And,
・
・
・
And,
_{(A # 3g-2,1,1% 3} , a # 3g-2,1,2% 3, a # 3g-2,1,3% 3),
(A _{# 3g-2,2,1} % 3, a _{# 3g-2,2,2} % 3, a _{# 3g-2,2,3} % 3), ...
(A _{# 3g-2, p, 1} % 3, a _{# 3g-2, p, 2} % 3, a _{# 3g-2, p, 3} % 3), ...
(A _{# 3g-2, n-1,1} % 3, a _{# 3g-2, n-1,2} % 3, a _{# 3g-2, n-1,3} % 3)
Any one of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become. (P = 1, 2, 3,..., N-1)
And,
(A _{# 3g-1,1,1} % 3, a _{# 3g-1,1,2} % 3, a _{# 3g-1,1,3} % 3),
(A _{# 3g-1,2,1} % 3, a _{# 3g-1,2,2} % 3, a _{# 3g-1,2,3} % 3), ...,
(A _{# 3g-1, p, 1} % 3, a _{# 3g-1, p, 2} % 3, a _{# 3g-1, p, 3} % 3), ...
(A _{# 3g-1, n-1,1} % 3, a _{# 3g-1, n-1,2} % 3, a _{# 3g-1, n-1,3} % 3)
Any one of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become. (P = 1, 2, 3,..., N-1)
And,
(A _{# 3g, 1,1} % 3, a _{# 3g, 1,2} % 3, a _{# 3g, 1,3} % 3),
(A _{# 3g, 2,1} % 3, a _{# 3g, 2,2} % 3, a _{# 3g, 2,3} % 3), ...
(A _{# 3g, p, 1} % 3, a _{# 3g, p, 2} % 3, a _{# 3g, p, 3} % 3), ...,
(A _{# 3g, n-1,1} % 3, a _{# 3g, n-1,2} % 3, a _{# 3g, n-1,3} % 3)
Any one of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become. (P = 1, 2, 3,..., N-1)

In addition, in the formulas (11-1) to (11-3g), the combination of the orders of P (D) satisfies the following condition.
(B _{# 1,1} % 3, b _{# 1,2} % 3),
(B _{# 2,1} % 3, b _{# 2,2} % 3),
(B _{# 3, 1} % 3, b _{# 3, 2} % 3), ...
(B _{# k, 1} % 3, b _{# k, 2} % 3), ...
(B _{# 3g-2,1} % 3, b _{# 3g-2,2} % 3),
(B _{# 3g-1,1} % 3, b _{# 3g-1,2} % 3),
(B _{# 3g, 1} % 3, b _{# 3g, 2} % 3) is
It becomes either (1, 2), (2, 1) (k = 1, 2, 3,..., 3g).

  <Condition # 3> for Expressions (11-1) to (11-3g) has the same relationship as <Condition # 2> for Expressions (9-1) to (9-3g). If the following condition (<condition # 4>) is added to the expressions (11-1) to (11-3g) in addition to <condition # 3>, an LDPC-CC having higher error correction capability is created. The possibility of being able to do increases.

<Condition # 4>
The following conditions are satisfied in the order of P (D) in formulas (11-1) to (11-3g).
(B _{# 1,1} % 3g, b _{# 1,2} % 3g),
(B _{# 2,1} % 3g, b _{# 2,2} % 3g),
(B _{# 3, 1} % 3 g, b _{# 3, 2} % 3 g), ...
(B _{# k, 1} % 3g, b _{# k, 2} % 3g), ...
(B _{# 3g-2, 1} % 3g, b _{# 3g-2, 2} % 3g),
(B _{# 3g-1,1} % 3g, b _{# 3g-1,2} % 3g),
The value of 6g orders (b _{# 3g, 1} % 3g, b _{# 3g, 2} % 3g) (the two orders constitute one set, so there are 6g orders constituting the 3g set), Of integers from 0 to 3g-1 (0, 1, 2, 3, 4, ..., 3g-2, 3g-1), multiples of 3 (that is, 0, 3, 6, ..., 3g) All values other than -3) exist.

  By the way, in the parity check matrix, if there is regularity at a position where “1” exists, but there is randomness, there is a high possibility that a good error correction capability can be obtained. Time-varying period 3g (g = 2, 3, 4, 5,...) Having parity check polynomials of equations (11-1) to (11-3g), and a coding rate of (n−1) / n ( In LDPC-CC (where n is an integer of 2 or more), if a code is created with <condition # 4> in addition to <condition # 3>, there is regularity at the position where “1” exists in the parity check matrix. However, since randomness can be given, the possibility that a good error correction capability can be obtained increases.

Next, in a time-varying period of 3 g (g = 2, 3, 4, 5,...) That can be easily encoded and has a relationship between parity bits and data bits at the same time. Consider LDPC-CC. At this time, assuming that the coding rate is (n-1) / n (n is an integer of 2 or more), the parity check polynomial of LDPC-CC can be expressed as follows.

In this _{case, X 1 (D), X} 2 (D), ··· X n-1 (D) is data _{(information)} X _1, X 2, a polynomial representation of ··· _{X n-1,} P (D) is a polynomial expression of parity. In formulas (13-1) to (13-3g), X ₁ (D), X ₂ (D),... X _n-1 (D), and P (D) each have three terms. Thus, a term of D ⁰ exists in X ₁ (D), X ₂ (D),... X _n−1 (D), P (D). (K = 1, 2, 3, ..., 3g)

However, in an LDPC-CC with a time varying period of 3 g and a coding rate (n−1) / n (n is an integer of 2 or more), the parity at time i is Pi and the information is X _{i, 1} , X _{i, 2} , ..., represented by Xi _{, n-1} . At this time, if i% 3g = k (k = 0, 1, 2,..., 3g−1), the parity check polynomial of Expression (13− (k + 1)) is established. For example, if i = 2, i% 3g = 2 (k = 2), and therefore equation (14) is established.

  At this time, if the following conditions (<condition # 5> and <condition # 6>) are satisfied, there is a high possibility that a code having a higher error correction capability can be created.

<Condition # 5>
In the formulas (13-1) to (13-3g), combinations of orders of X ₁ (D), X ₂ (D),... X _n-1 (D) satisfy the following conditions.
(A _{# 1,1,1} % 3, a _{# 1,1,2} % 3),
(A _{# 1,2,1} % 3, a _{# 1,2,2} % 3), ...
(A _{# 1, p, 1} % 3, a _{# 1, p, 2} % 3), ...,
(A _{# 1, n-1,1} % 3, a _{# 1, n-1,2} % 3) is
One of (1, 2) and (2, 1). (P = 1, 2, 3,..., N-1)
And,
_{(A # 2,1,1% 3, a} # 2,1,2% 3),
(A _{# 2,2,1} % 3, a _{# 2,2,2} % 3), ...
(A _{# 2, p, 1} % 3, a _{# 2, p, 2} % 3), ...,
(A _{# 2, n-1,1} % 3, a _{# 2, n-1,2} % 3) is
One of (1, 2) and (2, 1). (P = 1, 2, 3,..., N-1)
And,
(A _# 3, _1,1 % 3, a _{# 3, 1, 2} % 3),
(A _{# 3,2,1} % 3, a _{# 3,2,2} % 3), ...,
(A _{# 3, p, 1} % 3, a _{# 3, p, 2} % 3), ...,
(A _{# 3, n-1,1} % 3, a _{# 3, n-1,2} % 3) is
One of (1, 2) and (2, 1). (P = 1, 2, 3,..., N-1)
And,
・
・
・
And,
(A _{# k, 1,1} % 3, a _{# k, 1,2} % 3),
(A _{# k, 2,1} % 3, a _{# k, 2,2} % 3), ...
(A _{# k, p, 1} % 3, a _{# k, p, 2} % 3), ...,
(A _{# k, n-1,1} % 3, a _{# k, n-1,2} % 3)
One of (1, 2) and (2, 1). (P = 1, 2, 3,..., N-1) (hence, k = 1, 2, 3,..., 3g)
And,
・
・
・
And,
_{(A # 3g-2,1,1% 3} , a # 3g-2,1,2% 3),
(A _{# 3g-2,2,1} % 3, a _{# 3g-2,2,2} % 3), ...
(A _{# 3g-2, p, 1} % 3, a _{# 3g-2, p, 2} % 3), ...
(A _{# 3g-2, n-1,1} % 3, a _{# 3g-2, n-1,2} % 3) is
One of (1, 2) and (2, 1). (P = 1, 2, 3,..., N-1)
And,
(A _{# 3g-1,1,1} % 3, a _{# 3g-1,1,2} % 3),
(A _{# 3g-1,2,1} % 3, a _{# 3g-1,2,2} % 3), ...,
(A _{# 3g-1, p, 1} % 3, a _{# 3g-1, p, 2} % 3), ...
(A _{# 3g-1, n-1,1} % 3, a _{# 3g-1, n-1,2} % 3) is
One of (1, 2) and (2, 1). (P = 1, 2, 3,..., N-1)
And,
(A _{# 3g, 1,1} % 3, a _{# 3g, 1,2} % 3),
(A _{# 3g, 2,1} % 3, a _{# 3g, 2,2} % 3), ...
(A _{# 3g, p, 1} % 3, a _{# 3g, p, 2} % 3), ...
(A _{# 3g, n-1,1} % 3, a _{# 3g, n-1,2} % 3) is
One of (1, 2) and (2, 1). (P = 1, 2, 3,..., N-1)

In addition, in the formulas (13-1) to (13-3g), the combination of the orders of P (D) satisfies the following condition.
(B _{# 1,1} % 3, b _{# 1,2} % 3),
(B _{# 2,1} % 3, b _{# 2,2} % 3),
(B _{# 3, 1} % 3, b _{# 3, 2} % 3), ...
(B _{# k, 1} % 3, b _{# k, 2} % 3), ...
(B _{# 3g-2,1} % 3, b _{# 3g-2,2} % 3),
(B _{# 3g-1,1} % 3, b _{# 3g-1,2} % 3),
(B _{# 3g, 1} % 3, b _{# 3g, 2} % 3) is
It becomes either (1, 2), (2, 1) (k = 1, 2, 3,..., 3g).

  <Condition # 5> for Expressions (13-1) to (13-3g) has the same relationship as <Condition # 2> for Expressions (9-1) to (9-3g). If the following condition (<condition # 6>) is added to the expressions (13-1) to (13-3g) in addition to <condition # 5>, an LDPC-CC having high error correction capability can be created. The possibility increases.

<Condition # 6>
The following conditions are satisfied in the order of X ₁ (D) in formulas (13-1) to (13-3g).
(A _{# 1,1,1} % 3g, a _{# 1,1,2} % 3g),
_{(A # 2,1,1% 3g, a} # 2,1,2% 3g), ···,
(A _{# p, 1,1} % 3g, a _{# p, 1,2} % 3g), ...
6g values of (a _{# 3g, 1,1} % 3g, a _{# 3g, 1, 2} % 3g)
Of integers from 0 to 3g-1 (0, 1, 2, 3, 4, ..., 3g-2, 3g-1), multiples of 3 (that is, 0, 3, 6, ..., 3g) All values other than -3) exist. (P = 1, 2, 3, ..., 3g)
And,
The following conditions are satisfied in the order of X ₂ (D) in formulas (13-1) to (13-3g).
(A _{# 1,2,1} % 3g, a _{# 1,2,2} % 3g),
(A _{# 2,2,1} % 3g, a _{# 2,2,2} % 3g), ...,
(A _{# p, 2,1} % 3g, a _{# p, 2,2} % 3g), ...
The 6g values of (a _{# 3g, 2, 1} % 3g, a _{# 3g, 2, 2} % 3g)
Of integers from 0 to 3g-1 (0, 1, 2, 3, 4, ..., 3g-2, 3g-1), multiples of 3 (that is, 0, 3, 6, ..., 3g) All values other than -3) exist. (P = 1, 2, 3, ..., 3g)
And,
The following conditions are satisfied in the order of X ₃ (D) in the expressions (13-1) to (13-3g).
_{(A # 1,3,1% 3g, a} # 1,3,2% 3g),
_{(A # 2,3,1% 3g, a} # 2,3,2% 3g), ···,
(A _{# p, 3,1} % 3g, a _{# p, 3,2} % 3g), ...,
6g values of (a _{# 3g, 3,1} % 3g, a _{# 3g, 3,2} % 3g)
Of integers from 0 to 3g-1 (0, 1, 2, 3, 4, ..., 3g-2, 3g-1), multiples of 3 (that is, 0, 3, 6, ..., 3g) All values other than -3) exist. (P = 1, 2, 3, ..., 3g)
And,
・
・
・
And,
The following conditions are satisfied in the order of X _k (D) in Expressions (13-1) to (13-3g).
(A _{# 1, k, 1} % 3g, a _{# 1, k, 2} % 3g),
(A _{# 2, k, 1} % 3g, a _{# 2, k, 2} % 3g), ...
(A _{# p, k, 1} % 3g, a _{# p, k, 2} % 3g), ...
The 6g values of (a _{# 3g, k, 1} % 3g, a _{# 3g, k, 2} % 3g)
Of integers from 0 to 3g-1 (0, 1, 2, 3, 4, ..., 3g-2, 3g-1), multiples of 3 (that is, 0, 3, 6, ..., 3g) All values other than -3) exist. (P = 1, 2, 3, ..., 3g)
(K = 1, 2, 3,..., N-1)
And,
・
・
・
And,
The following conditions are satisfied in the order of X _n-1 (D) in formulas (13-1) to (13-3g).
(A _{# 1, n-1,1} % 3g, a _{# 1, n-1,2} % 3g),
(A _{# 2, n-1, 1} % 3g, a _{# 2, n-1, 2} % 3g), ...,
(A _{# p, n-1,1} % 3g, a _{# p, n-1,2} % 3g), ...
The 6g values (a _{# 3g, n-1, 1} % 3g, a _{# 3g, n-1, 2} % 3g)
Of integers from 0 to 3g-1 (0, 1, 2, 3, 4, ..., 3g-2, 3g-1), multiples of 3 (that is, 0, 3, 6, ..., 3g) All values other than -3) exist. (P = 1, 2, 3, ..., 3g)
And,
The following conditions are satisfied in the order of P (D) in formulas (13-1) to (13-3g).
(B _{# 1,1} % 3g, b _{# 1,2} % 3g),
(B _{# 2,1} % 3g, b _{# 2,2} % 3g),
(B _{# 3, 1} % 3 g, b _{# 3, 2} % 3 g), ...
(B _{# k, 1} % 3g, b _{# k, 2} % 3g), ...
(B _{# 3g-2, 1} % 3g, b _{# 3g-2, 2} % 3g),
(B _{# 3g-1,1} % 3g, b _{# 3g-1,2} % 3g),
(B _{# 3g, 1} % 3g, b _{# 3g, 2} % 3g)
Of integers from 0 to 3g-1 (0, 1, 2, 3, 4, ..., 3g-2, 3g-1), multiples of 3 (that is, 0, 3, 6, ..., 3g) All values other than -3) exist. (K = 1, 2, 3, ..., 3g)

  By the way, in the parity check matrix, if there is regularity at a position where “1” exists, but there is randomness, there is a high possibility that a good error correction capability can be obtained. A time-varying period 3g (g = 2, 3, 4, 5,...) Having a parity check polynomial of equations (13-1) to (13-3g), and a coding rate of (n−1) / n ( In LDPC-CC (where n is an integer of 2 or more), when a code is created by adding the condition of <condition # 6> in addition to <condition # 5>, the regularity is at the position where “1” exists in the parity check matrix. Since the randomness can be given while having the error rate, the possibility that a better error correction capability can be obtained increases.

  Also, instead of <Condition # 6>, <Condition # 6 ′> is used, that is, even if <Condition # 6 ′> is added in addition to <Condition # 5>, a higher error correction is possible. There is a high possibility that an LDPC-CC having the capability can be created.

<Condition # 6 '>
The following conditions are satisfied in the order of X ₁ (D) in formulas (13-1) to (13-3g).
(A _{# 1,1,1} % 3g, a _{# 1,1,2} % 3g),
_{(A # 2,1,1% 3g, a} # 2,1,2% 3g), ···,
(A _{# p, 1,1} % 3g, a _{# p, 1,2} % 3g), ...
6g values of (a _{# 3g, 1,1} % 3g, a _{# 3g, 1, 2} % 3g)
Of integers from 0 to 3g-1 (0, 1, 2, 3, 4, ..., 3g-2, 3g-1), multiples of 3 (that is, 0, 3, 6, ..., 3g) All values other than -3) exist. (P = 1, 2, 3, ..., 3g)
Or
The following conditions are satisfied in the order of X ₂ (D) in formulas (13-1) to (13-3g).
(A _{# 1,2,1} % 3g, a _{# 1,2,2} % 3g),
(A _{# 2,2,1} % 3g, a _{# 2,2,2} % 3g), ...,
(A _{# p, 2,1} % 3g, a _{# p, 2,2} % 3g), ...
The 6g values of (a _{# 3g, 2, 1} % 3g, a _{# 3g, 2, 2} % 3g)
Of integers from 0 to 3g-1 (0, 1, 2, 3, 4, ..., 3g-2, 3g-1), multiples of 3 (that is, 0, 3, 6, ..., 3g) All values other than -3) exist. (P = 1, 2, 3, ..., 3g)
Or
The following conditions are satisfied in the order of X ₃ (D) in the expressions (13-1) to (13-3g).
_{(A # 1,3,1% 3g, a} # 1,3,2% 3g),
_{(A # 2,3,1% 3g, a} # 2,3,2% 3g), ···,
(A _{# p, 3,1} % 3g, a _{# p, 3,2} % 3g), ...,
6g values of (a _{# 3g, 3,1} % 3g, a _{# 3g, 3,2} % 3g)
Of integers from 0 to 3g-1 (0, 1, 2, 3, 4, ..., 3g-2, 3g-1), multiples of 3 (that is, 0, 3, 6, ..., 3g) All values other than -3) exist. (P = 1, 2, 3, ..., 3g)
Or
・
・
・
Or
The following conditions are satisfied in the order of X _k (D) in Expressions (13-1) to (13-3g).
(A _{# 1, k, 1} % 3g, a _{# 1, k, 2} % 3g),
(A _{# 2, k, 1} % 3g, a _{# 2, k, 2} % 3g), ...
(A _{# p, k, 1} % 3g, a _{# p, k, 2} % 3g), ...
The 6g values of (a _{# 3g, k, 1} % 3g, a _{# 3g, k, 2} % 3g)
Of integers from 0 to 3g-1 (0, 1, 2, 3, 4, ..., 3g-2, 3g-1), multiples of 3 (that is, 0, 3, 6, ..., 3g) All values other than -3) exist. (P = 1, 2, 3, ..., 3g)
(K = 1, 2, 3,..., N-1)
Or
・
・
・
Or
The following conditions are satisfied in the order of X _n-1 (D) in formulas (13-1) to (13-3g).
(A _{# 1, n-1,1} % 3g, a _{# 1, n-1,2} % 3g),
(A _{# 2, n-1, 1} % 3g, a _{# 2, n-1, 2} % 3g), ...,
(A _{# p, n-1,1} % 3g, a _{# p, n-1,2} % 3g), ...
The 6g values (a _{# 3g, n-1, 1} % 3g, a _{# 3g, n-1, 2} % 3g)
Of integers from 0 to 3g-1 (0, 1, 2, 3, 4, ..., 3g-2, 3g-1), multiples of 3 (that is, 0, 3, 6, ..., 3g) All values other than -3) exist. (P = 1, 2, 3, ..., 3g)
Or
The following conditions are satisfied in the order of P (D) in formulas (13-1) to (13-3g).
(B _{# 1,1} % 3g, b _{# 1,2} % 3g),
(B _{# 2,1} % 3g, b _{# 2,2} % 3g),
(B _{# 3, 1} % 3 g, b _{# 3, 2} % 3 g), ...
(B _{# k, 1} % 3g, b _{# k, 2} % 3g), ...
(B _{# 3g-2, 1} % 3g, b _{# 3g-2, 2} % 3g),
(B _{# 3g-1,1} % 3g, b _{# 3g-1,2} % 3g),
(B _{# 3g, 1} % 3g, b _{# 3g, 2} % 3g)
Of integers from 0 to 3g-1 (0, 1, 2, 3, 4, ..., 3g-2, 3g-1), multiples of 3 (that is, 0, 3, 6, ..., 3g) All values other than -3) exist. (K = 1, 2, 3, ..., 3g)

  The LDPC-CC having a time varying period of 3 g and a coding rate (n−1) / n (n is an integer of 2 or more) has been described. Hereinafter, the condition of the degree of the parity check polynomial of the LDPC-CC having a time varying period of 3 g and a coding rate of ½ (n = 2) will be described.

As an LDPC-CC parity check polynomial with a time-varying period of 3 g (g = 1, 2, 3, 4,...) And a coding rate of ½ (n = 2), equations (15-1) to (15) 15-3g).

  At this time, X (D) is a polynomial expression of data (information) X, and P (D) is a polynomial expression of parity. Here, in equations (15-1) to (15-3g), the parity check polynomial is such that three terms exist in each of X (D) and P (D).

  When considered in the same manner as the LDPC-CC with the time varying period 3 and the LDPC-CC with the time varying period 6, the time varying period 3g represented by the parity check polynomials of the equations (15-1) to (15-3g), the coding rate In the case of 1/2 (n = 2) LDPC-CC, if the following condition (<condition # 2-1>) is satisfied, the possibility that higher error correction capability can be obtained increases.

However, in an LDPC-CC with a time varying period of 3 g and a coding rate of ½ (n = 2), the parity at time i is represented by Pi and the information is represented by X _{i, 1} . At this time, if i% 3g = k (k = 0, 1, 2,..., 3g−1), the parity check polynomial of Expression (15− (k + 1)) is established. For example, if i = 2, i% 3g = 2 (k = 2), and therefore equation (16) is established.

Moreover, in Formula (15-1)-Formula (15-3g), a _{# k, 1,1} , a _{# k, 1,2} , a _{# k, 1,3} is an integer (however, a _{# k, 1 , 1} ≠ a _{# k, 1,2} ≠ a _{# k, 1,3} ) (k = 1, 2, 3,..., 3g). Also, b _{# k, 1} , b _{# k, 2} , and b _{# k, 3} are integers (where b _{# k, 1} ≠ b _{# k, 2} ≠ b _{# k, 3} ). The parity check polynomial (k = 1, 2, 3,..., 3g) in Expression (15-k) is referred to as “check expression #k”, and a sub-matrix based on the parity check polynomial in Expression (15-k) K-th sub-matrix H _k . The first sub-matrix _{H 1,} second sub-matrix _{H 2,} third sub-matrix _H 3, considered ..., for LDPC-CC of varying period 3g when producing from a 3g submatrix _{H 3g.}

<Condition # 2-1>
In the formulas (15-1) to (15-3g), the combination of the orders of X (D) and P (D) satisfies the following condition.
(A _{# 1,1,1} % 3, a _{# 1,1,2} % 3, a _{# 1,1,3} % 3),
(B _{# 1,1} % 3, b _{# 1,2} % 3, b _{# 1,3} % 3)
Any one of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become.
And,
_{(A # 2,1,1% 3, a} # 2,1,2% 3, a # 2,1,3% 3),
(B _{# 2,1} % 3, b _{# 2,2} % 3, b _{# 2,3} % 3)
Any one of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become.
And,
_{(A # 3,1,1% 3, a} # 3,1,2% 3, a # 3,1,3% 3),
(B _{# 3, 1} % 3, b _{# 3, 2} % 3, b _{# 3, 3} % 3)
Any one of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become.
And,
・
・
・
And,
(A _{# k, 1,1} % 3, a _{# k, 1,2} % 3, a _{# k, 1,3} % 3),
(B _{# k, 1} % 3, b _{# k, 2} % 3, b _{# k, 3} % 3)
Any one of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become. (Thus, k = 1, 2, 3,..., 3g)
And,
・
・
・
And,
_{(A # 3g-2,1,1% 3} , a # 3g-2,1,2% 3, a # 3g-2,1,3% 3),
(B _{# 3g-2,1} % 3, b _{# 3g-2,2} % 3, b _{# 3g-2,3} % 3)
Any one of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become.
And,
(A _{# 3g-1,1,1} % 3, a _{# 3g-1,1,2} % 3, a _{# 3g-1,1,3} % 3),
(B _{# 3g-1,1} % 3, b _{# 3g-1,2} % 3, b _{# 3g-1,3} % 3)
Any one of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become.
And,
(A _{# 3g, 1,1} % 3, a _{# 3g, 1,2} % 3, a _{# 3g, 1,3} % 3),
(B _{# 3g, 1} % 3, b _{# 3g, 2} % 3, b _{# 3g, 3} % 3)
Any one of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become.

However, in consideration of the fact that encoding is performed easily, in the equations (15-1) to (15-3g),
Of the three (b _{# k, 1} % 3, b _{# k, 2} % 3, b _{# k, 3} % 3), one “0” may be present (where k = 1, 2,... 3g). At this time, if D ⁰ = 1 exists and b _{# k, 1} , b _{# k, 2} , and b _{# k, 3} are integers of 0 or more, the parity P can be obtained sequentially. Because it has.

In addition, in order to make it easy to search for a code having a high correction capability by relating the parity bit and the data bit at the same time, (a _{#k, 1,1} % 3, a _{# k, 1, It is} preferable that one “0” exists among the three of ₂ % 3, a _{# k, 1,3} % 3) (where k = 1, 2,..., 3g).

Next, consider an LDPC-CC with a time-varying period of 3 g (g = 2, 3, 4, 5,...) In consideration of easy encoding. At this time, if the coding rate is 1/2 (n = 2), the parity check polynomial of LDPC-CC can be expressed as follows.

At this time, X (D) is a polynomial expression of data (information) X, and P (D) is a polynomial expression of parity. Here, in equations (17-1) to (17-3g), the parity check polynomial is such that three terms exist in each of X and P (D). However, in an LDPC-CC with a time varying period of 3 g and a coding rate of ½ (n = 2), the parity at time i is represented by Pi and the information is represented by X _{i, 1} . At this time, if i% 3g = k (k = 0, 1, 2,..., 3g−1), the parity check polynomial of Expression (17− (k + 1)) is established. For example, if i = 2, i% 3g = 2 (k = 2), and therefore equation (18) is established.

  At this time, if <Condition # 3-1> and <Condition # 4-1> are satisfied, the possibility that a code having higher error correction capability can be created increases.

<Condition # 3-1>
In the formulas (17-1) to (17-3g), the combination of the orders of X (D) satisfies the following condition.
(A _{# 1,1,1} % 3, a _{# 1,1,2} % 3, a _{# 1,1,3} % 3) are (0, 1, 2), (0, 2, 1), ( 1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0).
And,
_{(A # 2,1,1% 3, a} # 2,1,2% 3, a # 2,1,3% 3) is (0,1,2), (0,2,1), ( 1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0).
And,
(A _{# 3,1,1} % 3, a _{# 3,1,2} % 3, a _{# 3,1,3} % 3) is (0,1,2), (0,2,1), ( 1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0).
And,
・
・
・
And,
(A _{# k, 1,1} % 3, a _{# k, 1,2} % 3, a _{# k, 1,3} % 3) is (0,1,2), (0,2,1), ( 1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0). (Thus, k = 1, 2, 3,..., 3g)
And,
・
・
・
And,
_{(A # 3g-2,1,1% 3} , a # 3g-2,1,2% 3, a # 3g-2,1,3% 3) is (0,1,2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0).
And,
(A _{# 3g-1,1,1} % 3, a _{# 3g-1,1,2} % 3, a _{# 3g-1,1,3} % 3) are (0,1,2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0).
And,
(A _{# 3g, 1,1} % 3, a _{# 3g, 1,2} % 3, a _{# 3g, 1,3} % 3) is (0,1,2), (0,2,1), ( 1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0).

In addition, in the formulas (17-1) to (17-3g), the combination of the orders of P (D) satisfies the following condition.
(B _{# 1,1} % 3, b _{# 1,2} % 3),
(B _{# 2,1} % 3, b _{# 2,2} % 3),
(B _{# 3, 1} % 3, b _{# 3, 2} % 3), ...
(B _{# k, 1} % 3, b _{# k, 2} % 3), ...
(B _{# 3g-2,1} % 3, b _{# 3g-2,2} % 3),
(B _{# 3g-1,1} % 3, b _{# 3g-1,2} % 3),
(B _{# 3g, 1} % 3, b _{# 3g, 2} % 3) is
It becomes either (1, 2), (2, 1) (k = 1, 2, 3,..., 3g).

  <Condition # 3-1> for Expressions (17-1) to (17-3g) has the same relationship as <Condition # 2-1> for Expressions (15-1) to (15-3g). If the following condition (<condition # 4-1>) is added to the expressions (17-1) to (17-3g) in addition to <condition # 3-1>, LDPC having higher error correction capability -The possibility of creating a CC increases.

<Condition # 4-1>
The following conditions are satisfied in the order of P (D) in the equations (17-1) to (17-3g).
(B _{# 1,1} % 3g, b _{# 1,2} % 3g),
(B _{# 2,1} % 3g, b _{# 2,2} % 3g),
(B _{# 3, 1} % 3 g, b _{# 3, 2} % 3 g), ...
(B _{# k, 1} % 3g, b _{# k, 2} % 3g), ...
(B _{# 3g-2, 1} % 3g, b _{# 3g-2, 2} % 3g),
(B _{# 3g-1,1} % 3g, b _{# 3g-1,2} % 3g),
(B _{# 3g, 1} % 3g, b _{# 3g, 2} % 3g)
Of integers from 0 to 3g-1 (0, 1, 2, 3, 4, ..., 3g-2, 3g-1), multiples of 3 (that is, 0, 3, 6, ..., 3g) All values other than -3) exist.

  By the way, in the parity check matrix, if there is regularity at a position where “1” exists, but there is randomness, there is a high possibility that a good error correction capability can be obtained. Time-varying period 3g (g = 2, 3, 4, 5,...) Having a parity check polynomial of formulas (17-1) to (17-3g), coding rate 1/2 (n = 2) In LDPC-CC, when a code is created with the condition of <condition # 4-1> in addition to <condition # 3-1>, the randomness is maintained while the regularity is present at the position where “1” exists in the parity check matrix. Therefore, the possibility that a better error correction capability can be obtained increases.

Next, in a time-varying period of 3 g (g = 2, 3, 4, 5,...) That can be easily encoded and has a relationship between parity bits and data bits at the same time. Consider LDPC-CC. At this time, if the coding rate is 1/2 (n = 2), the parity check polynomial of LDPC-CC can be expressed as follows.

At this time, X (D) is a polynomial expression of data (information) X, and P (D) is a polynomial expression of parity. In equations (19-1) to (19-3g), the parity check polynomial is such that three terms exist in each of X (D) and P (D), and X (D) and P (D) Will have a term of D ⁰ . (K = 1, 2, 3, ..., 3g)

However, in an LDPC-CC with a time varying period of 3 g and a coding rate of ½ (n = 2), the parity at time i is represented by Pi and the information is represented by X _{i, 1} . At this time, if i% 3g = k (k = 0, 1, 2,..., 3g−1), the parity check polynomial of Expression (19− (k + 1)) is established. For example, if i = 2, i% 3g = 2 (k = 2), and therefore equation (20) is established.

  At this time, if the following conditions (<condition # 5-1> and <condition # 6-1>) are satisfied, the possibility that a code having higher error correction capability can be created increases.

<Condition # 5-1>
In the formulas (19-1) to (19-3g), the combination of the orders of X (D) satisfies the following condition.
(A _{# 1,1,1} % 3, a _{# 1,1,2} % 3) is either (1,2) or (2,1).
And,
_{(A # 2,1,1% 3, a} # 2,1,2% 3) is a one of the (1,2), (2,1).
And,
(A _# 3, _{1, 1} % 3, a _{# 3, 1, 2} % 3) is either (1, 2) or (2, 1).
And,
・
・
・
And,
(A _{# k, 1,1} % 3, a _{# k, 1,2} % 3) is either (1,2) or (2,1). (Thus, k = 1, 2, 3,..., 3g)
And,
・
・
・
And,
_{(A # 3g-2,1,1% 3} , a # 3g-2,1,2% 3) is a one of the (1,2), (2,1).
And,
(A _{# 3g-1,1,1} % 3, a _{# 3g-1,1,2} % 3) is either (1,2) or (2,1).
And,
(A _{# 3g, 1,1} % 3, a _{# 3g, 1,2} % 3) is either (1,2) or (2,1).

In addition, in the formulas (19-1) to (19-3g), the combination of the orders of P (D) satisfies the following condition.
(B _{# 1,1} % 3, b _{# 1,2} % 3),
(B _{# 2,1} % 3, b _{# 2,2} % 3),
(B _{# 3, 1} % 3, b _{# 3, 2} % 3), ...
(B _{# k, 1} % 3, b _{# k, 2} % 3), ...
(B _{# 3g-2,1} % 3, b _{# 3g-2,2} % 3),
(B _{# 3g-1,1} % 3, b _{# 3g-1,2} % 3),
(B _{# 3g, 1} % 3, b _{# 3g, 2} % 3) is
It becomes either (1, 2), (2, 1) (k = 1, 2, 3,..., 3g).

  <Condition # 5-1> for Expressions (19-1) to (19-3g) has the same relationship as <Condition # 2-1> for Expressions (15-1) to (15-3g). When the following condition (<condition # 6-1>) is added to the expressions (19-1) to (19-3g) in addition to <condition # 5-1>, LDPC having higher error correction capability -The possibility of creating a CC increases.

<Condition # 6-1>
The following conditions are satisfied in the order of X (D) in the equations (19-1) to (19-3g).
(A _{# 1,1,1} % 3g, a _{# 1,1,2} % 3g),
_{(A # 2,1,1% 3g, a} # 2,1,2% 3g), ···,
(A _{# p, 1,1} % 3g, a _{# p, 1,2} % 3g), ...
6g values of (a _{# 3g, 1,1} % 3g, a _{# 3g, 1, 2} % 3g)
Of integers from 0 to 3g-1 (0, 1, 2, 3, 4, ..., 3g-2, 3g-1), multiples of 3 (that is, 0, 3, 6, ..., 3g) All values other than -3) exist. (P = 1, 2, 3, ..., 3g)
And,
The following conditions are satisfied in the order of P (D) in the equations (19-1) to (19-3g).
(B _{# 1,1} % 3g, b _{# 1,2} % 3g),
(B _{# 2,1} % 3g, b _{# 2,2} % 3g),
(B _{# 3, 1} % 3 g, b _{# 3, 2} % 3 g), ...
(B _{# k, 1} % 3g, b _{# k, 2} % 3g), ...
(B _{# 3g-2, 1} % 3g, b _{# 3g-2, 2} % 3g),
(B _{# 3g-1,1} % 3g, b _{# 3g-1,2} % 3g),
(B _{# 3g, 1} % 3g, b _{# 3g, 2} % 3g) 6g (3g x 2) values include
Of integers from 0 to 3g-1 (0, 1, 2, 3, 4, ..., 3g-2, 3g-1), multiples of 3 (that is, 0, 3, 6, ..., 3g) All values other than -3) exist. (K = 1, 2, 3, ..., 3g)

  By the way, in a parity check matrix, if there is regularity at a position where “1” exists, there is a high possibility that a good error correction capability can be obtained. In an LDPC-CC with a time varying period of 3 g (g = 2, 3, 4, 5,...) Having a parity check polynomial of equations (19-1) to (19-3g) and an encoding rate of 1/2, When a code is created by adding the condition of <condition # 6-1> in addition to <condition # 5-1>, a randomness is given to the check matrix with regularity at the position where “1” exists. Therefore, the possibility that a better error correction capability can be obtained increases.

  Also, instead of <Condition # 6-1>, <Condition # 6′-1> is used. That is, in addition to <Condition # 5-1>, <Condition # 6′-1> is added to create a code. Even so, the possibility that an LDPC-CC having higher error correction capability can be created increases.

<Condition # 6′-1>
The following conditions are satisfied in the order of X (D) in the equations (19-1) to (19-3g).
(A _{# 1,1,1} % 3g, a _{# 1,1,2} % 3g),
_{(A # 2,1,1% 3g, a} # 2,1,2% 3g), ···,
(A _{# p, 1,1} % 3g, a _{# p, 1,2} % 3g), ...
6g values of (a _{# 3g, 1,1} % 3g, a _{# 3g, 1, 2} % 3g)
Of integers from 0 to 3g-1 (0, 1, 2, 3, 4, ..., 3g-2, 3g-1), multiples of 3 (that is, 0, 3, 6, ..., 3g) All values other than -3) exist. (P = 1, 2, 3, ..., 3g)
Or
The following conditions are satisfied in the order of P (D) in the equations (19-1) to (19-3g).
(B _{# 1,1} % 3g, b _{# 1,2} % 3g),
(B _{# 2,1} % 3g, b _{# 2,2} % 3g),
(B _{# 3, 1} % 3 g, b _{# 3, 2} % 3 g), ...
(B _{# k, 1} % 3g, b _{# k, 2} % 3g), ...
(B _{# 3g-2, 1} % 3g, b _{# 3g-2, 2} % 3g),
(B _{# 3g-1,1} % 3g, b _{# 3g-1,2} % 3g),
(B _{# 3g, 1} % 3g, b _{# 3g, 2} % 3g)
Of integers from 0 to 3g-1 (0, 1, 2, 3, 4, ..., 3g-2, 3g-1), multiples of 3 (that is, 0, 3, 6, ..., 3g) All values other than -3) exist. (K = 1, 2, 3, ..., 3g)

As an example, Table 4 lists LDPC-CC having a good error correction capability and a coding rate of 1/2 and a time-varying period of 6.

The LDPC-CC having a time varying period g with good characteristics has been described above. LDPC-CC can obtain encoded data (codeword) by multiplying the information vector n by the generator matrix G. That is, the encoded data (code word) c can be expressed as c = n × G. Here, the generation matrix G is obtained in correspondence with a check matrix H designed in advance. Specifically, the generator matrix G is a matrix that satisfies G × H ^T = 0.

ここで、Ｄは、遅延演算子である。 For example, consider a convolutional code of coding rate 1/2 and generator polynomial G = [1 G ₁ (D) / G ₀ (D)]. In this case, _{G 1} is feed-forward polynomial, _{G 0} represents a feedback polynomial. When the polynomial expression of the information sequence (data) is X (D) and the polynomial expression of the parity sequence is P (D), the parity check polynomial is expressed by the following equation (21).

Here, D is a delay operator.

FIG. 5 describes information related to the (7, 5) convolutional code. The generation matrix of the (7, 5) convolutional code is expressed as G = [1 (D ² +1) / (D ² + D + 1)]. Therefore, the parity check polynomial is expressed by the following equation (22).

Here, the data at the time point i is represented as X _i , the parity is represented as P _i, and the transmission sequence W _i = (X _i , P _i ). Then, the transmission vector w = (X ₁ , P ₁ , X ₂ , P ₂ ,..., X _i , P _i ...) ^T. Then, from Equation (22), the check matrix H can be expressed as shown in FIG. At this time, the following relational expression (23) is established.

  Therefore, on the decoding side, BP (Belief Propagation) (reliability propagation) decoding as shown in Non-Patent Document 5 to Non-Patent Document 7, min-sum decoding approximating BP decoding, using check matrix H, Decoding using reliability propagation such as offset BP decoding, Normalized BP decoding, and shuffled BP decoding can be performed.

(Time-invariant / time-varying LDPC-CC based on convolutional code (coding rate (n-1) / n) (n: natural number))
The outline of the time-invariant / time-variant LDPC-CC based on the convolutional code will be described below.

Information _X 1 coding rate R = (n-1) / n, X 2, ···, the polynomial representation of the _{X n-1 X 1 (D} ), X 2 (D), ···, X n ₋₁ (D) and a polynomial expression of parity P is P (D), and a parity check polynomial expressed as shown in Expression (24) is considered.

In Expression (24), at this time, a _{p, p} (p = 1, 2,..., N−1; q = 1, 2,..., Rp) is, for example, a natural number, and _{ap, 1} ≠ a _{p, 2} ≠... ≠≠ a _{p, rp} is satisfied. _{Further, b q (q = 1,2,} ···, s) is a natural number, satisfying _{b 1 ≠ b 2 ≠ ··· ≠} b s. At this time, a code defined by a parity check matrix based on the parity check polynomial of Equation (24) is referred to herein as time invariant LDPC-CC.

ここで、ｉ＝０，１，・・・，ｍ−１である。 M different parity check polynomials based on Expression (24) are prepared (m is an integer of 2 or more). The parity check polynomial is expressed as follows.

Here, i = 0, 1,..., M−1.

ここで、「ｊ ｍｏｄ ｍ」は、ｊをｍで除算した余りである。 Then, the information X ₁ , X ₂ ,..., X _n−1 at the time point j is expressed as X _{1, j} , X _{2, j} ,..., X _{n−1, j,} and the parity P at the time point j is Pj and u _j = (X _{1, j} , X _{2, j} ,..., X _{n−1, j} , Pj) ^T. At this time, the information X _{1, j} , X _{2, j} ,..., X _{n−1, j} and the parity P _j at the time point j satisfy the parity check polynomial of Expression (26).

Here, “j mod m” is a remainder obtained by dividing j by m.

  A code defined by a parity check matrix based on the parity check polynomial of Equation (26) is referred to herein as time-varying LDPC-CC. At this time, the time-invariant LDPC-CC defined by the parity check polynomial of Equation (24) and the time-varying LDPC-CC defined by the parity check polynomial of Equation (26) sequentially register and exclude parity. It can be easily obtained by logical OR.

  For example, FIG. 6 shows the configuration of LDPC-CC parity check matrix H of time-varying period 2 based on equations (24) to (26) at a coding rate of 2/3. The two check polynomials having different time-varying periods 2 based on the formula (26) are named “check formula # 1” and “check formula # 2”. In FIG. 6, (Ha, 111) is a portion corresponding to “checking formula # 1”, and (Hc, 111) is a portion corresponding to “checking formula # 2”. Hereinafter, (Ha, 111) and (Hc, 111) are defined as sub-matrices.

  Thus, the LDPC-CC parity check matrix H of the proposed time-varying period 2 is represented by the first sub-matrix representing the parity check polynomial of “check equation # 1” and the parity check polynomial of “check equation # 2”. The second sub-matrix can be defined. Specifically, in the check matrix H, the first sub-matrix and the second sub-matrix are alternately arranged in the row direction. In the case of a coding rate of 2/3, as shown in FIG. 6, in the i-th row and the i + 1-th row, the sub-matrix is shifted to the right by 3 columns.

In the case of time-varying LDPC-CC with a time-varying period 2, the i-th row sub-matrix and the i + 1-th row sub-matrix are different sub-matrices. That is, one of the sub-matrices (Ha, 11) or (Hc, 11) is the first sub-matrix, and the other is the second sub-matrix. The transmission vector u is expressed as u = (X _1,0 , X _2,0 , P ₀ , X _1,1 , X _2,1 , P ₁ ,..., X _{1, k} , X _{2, k} , P _k ,...) If ^T , Hu = 0 holds (see equation (23)).

Next, consider an LDPC-CC in which the time-varying period is m when the coding rate is 2/3. As in the case of time-varying period 2, m parity check polynomials represented by Expression (24) are prepared. Then, “inspection formula # 1” represented by formula (24) is prepared. Similarly, “checking formula # 2” to “checking formula #m” represented by formula (24) are prepared. The data X and the parity P at the time point _{mi + 1} are represented as X _{mi + 1} and P _{mi + 1} , respectively. The data X and the parity P at the time point mi + 2 are respectively represented as X _{mi + 2} and P _{mi + 2} ..., And the data X and the parity P at the time point mi + m. Are represented as X _{mi + m} and P _{mi + m} , respectively (i: integer).

At this time, the parity P _{mi + 1} at the time point mi + 1 is obtained using the “check equation # 1”, the parity P _{mi + 2} at the time point mi + 2 is obtained using the “check equation # 2,” and the parity P _{mi + m} at the time point mi + m is obtained. Consider an LDPC-CC obtained using “checking formula #m”. Such LDPC-CC codes are:
The encoder can be easily configured, and the parity can be obtained sequentially. Advantages include reduction of the termination bits and improvement in reception quality at the time of puncturing at the termination.

FIG. 7 shows the configuration of the LDPC-CC parity check matrix having the coding rate of 2/3 and the time varying period m described above. In FIG. 7, (H ₁ , 111) is a portion corresponding to “checking formula # 1”, (H ₂ , 111) is a portion corresponding to “checking formula # 2”, (H _m , 111) is a portion corresponding to “checking formula #m”. Hereinafter, (H ₁ , 111) is defined as the first sub-matrix, (H ₂ , 111) is defined as the second sub-matrix,..., (H _m , 111) is defined as the m-th sub-matrix. To do.

  Thus, the LDPC-CC parity check matrix H of the proposed time-varying period m represents the first sub-matrix representing the parity check polynomial of “check formula # 1” and the parity check polynomial of “check formula # 2”. , And the m-th sub-matrix representing the parity check polynomial of “check equation #m”. Specifically, in the check matrix H, the first sub-matrix to the m-th sub-matrix are periodically arranged in the row direction (see FIG. 7). In the case of a coding rate of 2/3, the sub-matrix is shifted to the right by three columns in the i-th row and the i + 1-th row (see FIG. 7).

The transmission vector u is expressed as u = (X _1,0 , X _2,0 , P ₀ , X _1,1 , X _2,1 , P ₁ ,..., X _{1, k} , X _{2, k} , P _k ,...) If ^T , Hu = 0 holds (see equation (23)).

  In the above description, the case of the coding rate 2/3 has been described as an example of the time-invariant / time-varying LDPC-CC based on the convolutional code of the coding rate (n-1) / n. Thus, it is possible to create a time-invariant / time-variant LDPC-CC parity check matrix based on a convolutional code with a coding rate (n−1) / n.

That is, in the case of the coding rate 2/3, in FIG. 7, (H ₁ , 111) is a portion (first sub-matrix) corresponding to “check equation # 1”, and (H ₂ , 111) is “check”. A part (second sub-matrix) corresponding to “Expression # 2”,..., (H _m , 111) is a part (m-th sub-matrix) corresponding to “check expression #m”, In the case of the coding rate (n-1) / n, it is as shown in FIG. That is, the portion (first sub-matrix) corresponding to “check equation # 1” is represented by (H ₁ , 11... 1), and “check equation #k” (k = 2, 3,... , M) (kth sub-matrix) is represented by (H _k , 11... 1). At this time, in the k-th sub-matrix, the number of “1” s in the portion excluding H _k is n−1. In the parity check matrix H, the sub-matrix is shifted to the right of n−1 columns in the i-th row and the i + 1-th row (see FIG. 8).

The transmit vector _{u, u = (X 1,0,} X 2,0, ···, X n-1,0, P 0, X 1,1, X 2,1, ···, X n-1 _{, 1, P 1, ···,} X 1, k, X 2, k, ···, X n-1, k, P k, ····) When ^T, Hu = 0 is satisfied ( (Refer Formula (23)).

  As an example, FIG. 9 shows a configuration example of an LDPC-CC encoder when the coding rate R = 1/2. As shown in FIG. 9, the LDPC-CC encoder 100 mainly includes a data operation unit 110, a parity operation unit 120, a weight control unit 130, and a mod2 adder (exclusive OR operation) unit 140.

  The data operation unit 110 includes shift registers 111-1 to 111-M and weight multipliers 112-0 to 112-M.

  The parity calculation unit 120 includes shift registers 121-1 to 121-M and weight multipliers 122-0 to 122-M.

The shift registers 111-1 to 111 -M and 121-1 to 121 -M are registers that hold v _{1, ti} , v _{2, ti} (i = 0,..., M), respectively. At the timing when the input is input, the stored value is output toward the right shift register, and the value output from the left shift register is newly stored. The initial state of the shift register is all zero.

The weight multipliers 112-0 to 112-M and 122-0 to 122-M set the values of h ₁ ^(m) and h ₂ ^(m) to 0/1 in accordance with the control signal output from the weight control unit 130. Switch to.

The weight control unit 130 outputs the values of h ₁ ^(m) and h ₂ ^{(m) at} the timing based on the check matrix held therein, and the weight multipliers 112-0 to 112 -M and 122-0. Supply toward ~ 122-M.

The mod2 adder 140 adds all the mod2 calculation results to the outputs of the weight multipliers 112-0 to 112-M and 122-0 to 122-M, and calculates p _i .

  By adopting such a configuration, LDPC-CC encoder 100 can perform LDPC-CC encoding according to a parity check matrix.

  Note that when the rows of the parity check matrix held by the weight controller 130 are different for each row, the LDPC-CC encoder 100 is a time varying convolutional encoder. Further, in the case of LDPC-CC with a coding rate (q−1) / q, (q−1) data operation units 110 are provided, and a mod2 adder 140 mod2 adds the output of each weight multiplier ( (Exclusive OR operation) may be performed.

(Embodiment 2)
Next, in the present embodiment, an LDPC-CC search method capable of supporting a plurality of coding rates with a low computation scale in the encoder / decoder will be described. By using the LDPC-CC searched by the method described below, the decoder can achieve high data reception quality.

  The LDPC-CC search method in the present embodiment is based on, for example, LDPC-CC having a coding rate of 1/2 among LDPC-CCs having good characteristics as described above, and coding rate 2/3, 3/4, 4/5,..., (Q−1) / q LDPC-CCs are sequentially searched. Thus, in the encoding and decoding processes, by preparing an encoder and a decoder at the highest encoding rate (q-1) / q, the highest encoding rate (q-1 ) / Q encoding rate (s-1) / s (s = 2, 3,..., Q-1) can be encoded and decoded.

  In the following description, an LDPC-CC with a time varying period of 3 is used as an example. As described above, the LDPC-CC having the time-varying period 3 has a very good error correction capability.

(LDPC-CC search method)
(1) Coding rate 1/2
First, an LDPC-CC with a coding rate of 1/2 is selected as a base LDPC-CC. As the LDPC-CC having a coding rate of 1/2, the LDPC-CC having good characteristics as described above is selected.

Below, the case where the parity check polynomial represented by Formula (27-1)-Formula (27-3) is selected as a parity check polynomial of LDPC-CC of the basic coding rate 1/2 is demonstrated. (Examples of Expressions (27-1) to (27-3) are represented in the same format as the above (LDPC-CC having good characteristics), and therefore, LDPC-CC with a time-varying period of 3 is 3 (It can be defined by two parity check polynomials.)

Equations (27-1) to (27-3) are examples of an LDPC-CC parity check polynomial having a good time-varying period of 3 and a coding rate of 1/2, as described in Table 3. . Then, as described in the above (LDPC-CC having good characteristics), the information X ₁ at the time point j is expressed as X _{1, j} , the parity P at the time point j is expressed as P _j , and u _j = (X _{1 , J} , Pj) Let ^T. At this time, information X _{1, j} and parity P _{j at time j} are
“When j mod 3 = 0, the parity check polynomial of Expression (27-1) is satisfied.”
“When j mod 3 = 1, the parity check polynomial of Expression (27-2) is satisfied.”
“When j mod 3 = 2, the parity check polynomial of Expression (27-3) is satisfied.”
At this time, the relationship between the parity check polynomial and the check matrix is the same as that described in the above (LDPC-CC having good characteristics).

(2) Coding rate 2/3
Next, an LDPC-CC parity check polynomial with a coding rate of 2/3 is created based on a parity check polynomial with a coding rate of ½ with good characteristics. Specifically, an LDPC-CC parity check polynomial with a coding rate of 2/3 includes a parity check polynomial with a coding rate of 1/2.

A parity check polynomial of an LDPC-CC with a coding rate of 2/3 when the equations (27-1) to (27-3) are used for the base LDPC-CC with a coding rate of 1/2 is expressed by the equation (28-). 1) to Expression (28-3).

The parity check polynomials shown in Expression (28-1) to Expression (28-3) adopt a configuration in which the term X ₂ (D) is added to Expression (27-1) to Expression (27-3), respectively. . The parity check polynomial of LDPC-CC with a coding rate of 2/3 using the equations (28-1) to (28-3) is the basis of a parity check polynomial with a coding rate of 3/4, which will be described later.

In the equations (28-1) to (28-3), each order of X ₂ (D), (α1, β1), (α2, β2), (α3, β3) is the same as the above condition (< If conditions are set so as to satisfy the conditions # 1> to <condition # 6>, LDPC-CC with good characteristics can be obtained even at a coding rate of 2/3.

As described in the above (LDPC-CC having good characteristics), the information X _{1 and} X ₂ at the time point j are expressed as X _{1, j and} X _{2, j,} and the parity P at the time point j is set as P j In this case, u _j = (X _{1, j} , X _{2, j} , Pj) ^T. At this time, information X _{1, j,} X _{2, j} and parity P _{j at time j} are
“When j mod 3 = 0, the parity check polynomial of Expression (28-1) is satisfied.”
“When j mod 3 = 1, the parity check polynomial of Expression (28-2) is satisfied.”
“When j mod 3 = 2, the parity check polynomial of Expression (28-3) is satisfied.”
At this time, the relationship between the parity check polynomial and the check matrix is the same as that described in the above (LDPC-CC having good characteristics).

(3) Coding rate 3/4
Next, an LDPC-CC parity check polynomial with a coding rate of 3/4 is created based on the parity check polynomial with a coding rate of 2/3. Specifically, an LDPC-CC parity check polynomial with an encoding rate of 3/4 includes a parity check polynomial with an underlying encoding rate of 2/3.

A parity check polynomial of an LDPC-CC with a coding rate of 3/4 when the equations (28-1) to (28-3) are used for an LDPC-CC with a base coding rate of 2/3 is given by the equation (29- 1) to formula (29-3).

The parity check polynomials shown in Expressions (29-1) to (29-3) adopt a configuration in which the term X ₃ (D) is added to Expressions (28-1) to (28-3), respectively. . Note that in the equations (29-1) to (29-3), each order of X ₃ (D), (γ1, δ1), (γ2, δ2), (γ3, δ3) is LDPC with good characteristics. When setting is made so as to satisfy the condition of the order of CC (<condition # 1> to <condition # 6>, etc.), an LDPC-CC with good characteristics can be obtained even at a coding rate of 3/4 .

Then, as described above (LDPC-CC having good characteristics), the information X _1, X _2, X ₃ at the time point _j is represented as X _{1, j,} X _{2, j,} X _{3, j} , The parity P at the time point j is represented as Pj, and u _j = (X _{1, j} , X _{2, j} , X _{3, j} , Pj) ^T. At this time, the information X1 _{, j,} X2 _{, j,} X3 _{, j} and the parity Pj of the time point _j are
“When j mod 3 = 0, the parity check polynomial of Expression (29-1) is satisfied.”
“When j mod 3 = 1, the parity check polynomial of equation (29-2) is satisfied.”
“When j mod 3 = 2, the parity check polynomial of equation (29-3) is satisfied.”
At this time, the relationship between the parity check polynomial and the check matrix is the same as that described in the above (LDPC-CC having good characteristics).

Formulas (30-1) to (30- (q-1)) represent general formulas of the parity check polynomial of the LDPC-CC having the time-varying period g when searching as described above.

  However, since the expression (30-1) is expressed by a general expression, it is expressed as the expression (30-1), but as described above (LDPC-CC having good characteristics). In fact, since the time-varying period is g, Expression (30-1) is expressed by g parity check polynomials. (As described in the present embodiment, for example, in the case of time-varying period 3, it is expressed by three parity check polynomials as in equations (27-1) to (27-3).) Similar to Expression (30-1), Expressions (30-2) to (30- (q-1)) are also expressed by g parity check polynomials because the time-varying period is g.

  Here, g parity check polynomials of Expression (30-1) are expressed by Expression (30-1-0), Expression (30-1-1), Expression (30-1-2),. 30-1- (g-2)) and the expression (30-1- (g-1)).

  Similarly, equation (30-w) is expressed by g parity check polynomials (w = 2, 3,..., Q−1). Here, g parity check polynomials of Expression (30-w) are expressed by Expression (30-w-0), Expression (30-w-1), Expression (30-w-2),. 30-w- (g-2)) and expression (30-w- (g-1)).

In addition, in Formula (30-1) to Formula (30- (q-1)), X _{1, i} , X _{2, i} ,..., X _{q−1, i} are information X ₁ at time point i, X ₂ ,..., X _q−1 , and P _i indicates the parity P at time i. A _{Xr, k} (D) is a time i of coding rate (r−1) / r (r = 2, 3,..., Q (q is a natural number of 3 or more)), and k = i mod g Is the term of X _r (D) in the parity check polynomial of k obtained as B _k (D) is a term of P (D) in the parity check polynomial of k obtained as time i of coding rate (r−1) / r and k = i mod g. “I mod g” is a remainder obtained by dividing i by g.

  That is, Expression (30-1) is an LDPC-CC parity check polynomial of time-varying period g corresponding to coding rate 1/2, and Expression (30-2) corresponds to coding rate 2/3. Is a parity check polynomial of an LDPC-CC with a time-varying period g, and Equation (30- (q-1)) is an LDPC- with a time-varying period g corresponding to the coding rate (q-1) / q. It is a parity check polynomial of CC.

  Thus, based on Equation (30-1), which is a parity check polynomial of an LDPC-CC with good coding rate 1/2, a parity check polynomial of an LDPC-CC with a coding rate of 2/3 ( 30-2) is generated.

  Further, based on the parity check polynomial (30-2) of the LDPC-CC with the coding rate 2/3, the parity check polynomial (30-3) of the LDPC-CC with the coding rate 3/4 is generated. In the same manner, an LDPC-CC parity check polynomial of coding rate r / (r + 1) is generated based on LDPC-CC of coding rate (r−1) / r. (R = 2, 3, ..., q-2, q-1)

  Another expression will be given for the above parity check polynomial construction method. Consider an LDPC-CC with a time-varying period g of coding rate (y-1) / y and an LDPC-CC with a time-varying period g of coding rate (z-1) / z. However, the maximum coding rate is (q-1) / q among the coding rates for the common use of the encoder circuit and the common use of the decoder circuit, and g is 2 or more. An integer, y is an integer of 2 or more, z is an integer of 2 or more, and a relationship of y <z ≦ q is established. Note that the sharing of the circuit of the encoder is the sharing of the circuit inside the encoder, not the sharing of the circuit of the encoder and the decoder.

At this time, Expressions (30-w-0) and Expressions (30-w) expressing g parity check polynomials described when the expressions (30-1) to (30- (q-1)) are described. -1), formula (30-w-2), ..., formula (30-w- (g-2)), formula (30-w- (g-1)), w = y-1 In this case, g parity check polynomials are expressed by Expression (31-1) to Expression (31-g).

  In Formula (31-1) to Formula (31-g), Formula (31-w) and Formula (31-w ′) are equivalent formulas, and are hereinafter described as Formula (31-w). May be replaced with the formula (31-w ′) (w = 1, 2,..., G).

Then, as described in the above (LDPC-CC having good characteristics), information X _1, X _2, ..., X _y−1 at time point j is expressed as X _{1, j,} X _{2, j,.} .., X _{y−1, j} , where the parity P at time _j is expressed as Pj, and u _j = (X _{1, j} , X _{2, j,} ..., X _{y−1, j} , Pj) ^T And At this time, the information X1 _{, j,} X2 _{, j,} ..., _{Xy-1, j of} the time point _j and the parity _Pj are
“When j mod g = 0, the parity check polynomial of Expression (31-1) is satisfied.”
“When j mod g = 1, the parity check polynomial of Expression (31-2) is satisfied.”
“When j mod g = 2, the parity check polynomial of Expression (31-3) is satisfied.”
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“When j mod g = k, the parity check polynomial of Expression (31− (k + 1)) is satisfied.”
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“When j mod g = g−1, the parity check polynomial of Expression (31-g) is satisfied.”
At this time, the relationship between the parity check polynomial and the check matrix is the same as that described in the above (LDPC-CC having good characteristics).

Next, Expressions (30-w-0) and Expressions (30-w) expressing g parity check polynomials described when the expressions (30-1) to (30- (q-1)) are described. -1), formula (30-w-2), ..., formula (30-w- (g-2)), and formula (30-w- (g-1)), w = z-1 In this case, g parity check polynomials are expressed by equations (32-1) to (32-g). (From the relationship of y <z ≦ q, it can be expressed as Expression (32-1) to Expression (32-g).)

  In Formula (32-1) to Formula (32-g), Formula (32-w) and Formula (32-w ′) are equivalent formulas, and are hereinafter described as Formula (32-w). May be replaced with the equation (32-w ′) (w = 1, 2,..., G).

Then, as described in the above (LDPC-CC with good characteristics), information _{X 1,} X 2 at time _{j, ···, X y-1} , ···, X s, ···, _Xz-1 is represented as X1 _{, j,} X2 _{, j,} ..., _{Xy-1, j,} ..., Xs _{, j,} ..., _{Xz-1, j,} and time j the parity P represents a Pj _{in, u j = (X 1,} j, X 2, j, ···, X y-1, j, ···, X s, j, ···, X z-1 _{, J} , Pj) ^T (therefore, from the relationship of y <z ≦ q, s = y, y + 1, y + 2, y + 3,..., Z-3, z-2, z-1). At this time, information _X 1 point _{j, j, X 2, j} , ···, X y-1, j, ···, X s, j, ···, X z-1, j and parity P _j is
“When j mod g = 0, the parity check polynomial of Expression (32-1) is satisfied.”
“When j mod g = 1, the parity check polynomial of equation (32-2) is satisfied.”
“When j mod g = 2, the parity check polynomial of Expression (32-3) is satisfied.”
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“When j mod g = k, the parity check polynomial of Expression (32− (k + 1)) is satisfied.”
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“When j mod g = g−1, the parity check polynomial of Expression (32-g) is satisfied.” At this time, the relationship between the parity check polynomial and the check matrix is the above-mentioned (LDPC-CC having good characteristics). This is the same as the case described above.

  In the case where the above relationship holds, LDPC-CC with a time-varying period g at a coding rate (y-1) / y and LDPC-CC with a time-varying period g at a coding rate (z-1) / z. When the following conditions are satisfied, an LDPC-CC encoder having a time varying period g at a coding rate (y-1) / y and a time varying period g at a coding rate (z-1) / z. An LDPC-CC encoder can share a circuit, and an LDPC-CC decoder having a time-varying period g at a coding rate (y-1) / y, and a coding rate (z- 1) An LDPC-CC decoder with a time-varying period g at / z can share a circuit. The conditions are as follows.

First, the following relationship is established between Expression (31-1) and Expression (32-1).
"What is an _{A X1,0} (D) of the formula (31-1) _{A X1,0} of (D) and formula (32-1), the equal sign is established."
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_{"A Xf} of formula _{A Xf,} 0 the (31-1) (D) and Formula _(32-1), 0 (D) is equality established."
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"Equation (31-1) of _{A Xy-1, 0} (D) and _{A Xy-1, 0} (D) of the formula (32-1), the equality is satisfied."
That is, the above relationship is established at f = 1, 2, 3,.

In addition, the following relationship holds for parity.
_"B 0 and (D) is of formula (31-1) _B 0 of (D) and Formula (32-1), equality is established."

Similarly, the following relationship is established between Expression (31-2) and Expression (32-2).
"What is an _{A X1,1} (D) of the formula (31-2) _{A X1,1} of (D) and formula (32-2), the equal sign is established."
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_{"A Xf} of formula _(31-2), 1 (D) and _{A Xf} of the formula _(32-2), 1 and the (D), equality is established."
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"Equation (31-2) of _{A Xy-1, 1} (D) and _{A Xy-1, 1} (D) of the formula (32-2), the equality is satisfied."
That is, the above relationship is established at f = 1, 2, 3,.

In addition, the following relationship holds for parity.
_"B 1 and (D) is of formula (31-2) _B 1 of (D) and Formula (32-2), equality is established."

(Omitted)

Similarly, the following relationship is established between Expression (31-h) and Expression (32-h).
"The formula _{A X1, h-1 (D} ) of the _{(31-h) A X1,} h-1 (D) and formula (32-h), equality is established."
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_{"A Xf} of the formula _{(31-h), h-} 1 (D) and _{A Xf} of the formula _(32-h), the _h-1 (D), equality is established."
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"Formula _{A Xy-1} of _{(31-h), h-} 1 (D) and Formula _{A Xy-1} of _{(32-h), h-} 1 (D) , the equality is satisfied."
That is, the above relationship is established at f = 1, 2, 3,.

In addition, the following relationship holds for parity.
"Formula (31-h) of _{B h-1} (D) and Formula _{B h-1} (D) of the (32-h), the equality is satisfied."

(Omitted)

Similarly, the following relationship is established between Expression (31-g) and Expression (32-g).
"The formula _{A X1, g-1 (D} ) of the _{(31-g) A X1,} g-1 (D) and formula (32-g), equality is established."
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_{"A Xf} of the formula _{(31-g), g-} 1 (D) and _{A Xf} of the formula _(32-g), and the _g-1 (D), the equality holds."
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"Formula _{A Xy-1} of _{(31-g), g-} 1 (D) and formula (32-g) of the _{A Xy-1, g-1} (D) , the equality is satisfied."
That is, the above relationship is established at f = 1, 2, 3,.

In addition, the following relationship holds for parity.
“The equal sign is established between B _g-1 (D) in the formula (31-g) and B _g-1 (D) in the formula (32-g).”
(Thus, h = 1, 2, 3,..., G-2, g-1, and g.)

  When the above relationship is established, the LDPC-CC encoder of the time varying period g at the coding rate (y-1) / y and the time varying period g of the coding rate (z-1) / z. An LDPC-CC encoder can share a circuit, and an LDPC-CC decoder and a coding rate (z-1) having a time varying period g at a coding rate (y-1) / y. The circuit can be shared with the LDPC-CC decoder having a time-varying period g at) / z. However, the method for sharing the encoder circuit and the method for sharing the decoder circuit will be described in detail later (configuration of the encoder and decoder).

Table 5 shows an example of a parity check polynomial of an LDPC-CC satisfying the above-described conditions and having a time-varying period of 3, and a corresponding coding rate of 1/2, 2/3, 3/4, and 5/6. However, the format of the parity check polynomial is represented in the same format as that in Table 3. As a result, when the transmission apparatus and the reception apparatus support the coding rates of 1/2, 2/3, 3/4, and 5/6 (or encoding of two or more of the four coding rates). (If the transmitter and receiver support the rate)) Reduction in computation scale (circuit scale) (Distributed codes, while being able to share the encoder circuit and the decoder circuit) The circuit scale can be reduced), and the reception apparatus can obtain high data reception quality.

  It will be described that the LDPC-CC having the time varying period 3 in Table 5 satisfies the above conditions. For example, consider the LDPC-CC with the time varying period 3 at the coding rate 1/2 in Table 5 and the LDPC-CC with the time varying period 3 at the coding rate 2/3 in Table 5. That is, y = 2 in (31-1) to (31-g), and z = 3 in (32-1) to (32-g).

Then, from the LDPC-CC of the time-varying period 3 at the coding rate 1/2 in Table 5, A _X1,0 (D) in Expression (31-1) becomes D ³⁷³ + D ⁵⁶ +1, and the coding rate in Table 5 From LDPC-CC with a time-varying period of 3 in 2/3, A _X1,0 (D) in equation (32-1) becomes D ³⁷³ + D ⁵⁶ +1, and “A _{X1,0 in} equation (31-1) (D) And A _X1,0 (D) in the equation (32-1) is an equal sign. "

Further, from LDPC-CC with a time varying period of 3 at a coding rate of 1/2 in Table 5, B ₀ (D) in Equation (31-1) becomes D ⁴⁰⁶ + D ²¹⁸ +1, and the coding rate of 2 / 3 becomes B ₀ (D) = D ⁴⁰⁶ + D ²¹⁸ +1 in the equation (32-1) from the LDPC-CC of the time varying period 3 in “3”, and “B ₀ (D) in the equation (31-1) and the equation (32− The equal sign holds for B ₀ (D) in 1). ”

Similarly, from the LDPC-CC of the time varying period 3 at the coding rate 1/2 in Table 5, A _X1,1 (D) = D ⁴⁵⁷ + D ¹⁹⁷ +1 in the equation (31-2) From the LDPC-CC of the time-varying period 3 at the rate 2/3, A _X1,1 (D) = D ⁴⁵⁷ + D ¹⁹⁷ +1 in the equation (32-2) becomes “A _X1,1 (D in the equation (31-2)” ) And A _X1,1 (D) in equation (32-2) are equal. "

Further, from LDPC-CC with a time varying period of 3 at a coding rate of 1/2 in Table 5, B ₁ (D) in Equation (31-2) becomes D ⁴⁹¹ + D ²² +1, and the coding rate of 2 / 3, B ₁ (D) = D ⁴⁹¹ + D ²² +1 in the equation (32-2) is obtained from the LDPC-CC of the time-varying period 3, and “B ₁ (D) in the equation (31-2) and the equation (32− The equal sign holds for B ₁ (D) in 2). ”

Similarly, from the LDPC-CC of the time varying period 3 at the coding rate 1/2 in Table 5, A _X1,2 (D) in the equation (31-3) becomes D ⁴⁸⁵ + D ⁷⁰ +1, and the coding in Table 5 is performed. From the LDPC-CC of the time-varying period 3 at the rate 2/3, A _X1,2 (D) in the equation (32-3) = D ⁴⁸⁵ + D ⁷⁰ +1, and “A _{X1,2 in the} equation (31-3) ( D) and A _X1,2 (D) in equation (32-3) are equal. "

Further, from the LDPC-CC of the time varying period 3 at the coding rate 1/2 in Table 5, B ₂ (D) in the equation (31-3) becomes D ²³⁶ + D ¹⁸¹ +1, and the coding rate 2 / 3, B ₂ (D) in the equation (32-3) becomes D ²³⁶ + D ¹⁸¹ +1, and “B ₂ (D) in the equation (31-3) and the equation (32− The equal sign holds for B ₂ (D) in 3). ”

  As can be seen from the above, the LDPC-CC with the time-varying period 3 at the coding rate 1/2 in Table 5 and the LDPC-CC with the time-varying period 3 in the coding rate 2/3 in Table 5 are the above conditions. Can be confirmed.

  Similarly to the above, in the LDPC-CC having the time varying period 3 in Table 5, the time varying period 3 of two different coding rates out of the coding rates 1/2, 2/3, 3/4, and 5/6. If the LDPC-CC is selected and verification is made as to whether the above condition is satisfied, it can be confirmed that the above condition is satisfied in any selection pattern.

  Since LDPC-CC is a type of convolutional code, termination and tail biting are required to ensure reliability in decoding information bits. Here, a case where a method of setting the state of data (information) X to zero (hereinafter referred to as “Information-zero-termination”) is considered.

  FIG. 10 shows a method of “Information-zero-termination”. As shown in FIG. 10, the information bit (final transmission bit) to be transmitted last in the information sequence to be transmitted is Xn (110). When the transmission apparatus transmits data only up to the parity bit generated by the encoder in accordance with the final information bit Xn (110), when the reception apparatus performs decoding, the reception quality of information is greatly deteriorated. . To solve this problem, encoding is performed assuming that the information bits after the last information bit Xn (110) (referred to as “virtual information bits”) are “0”, and a parity bit (130) is generated. To do.

  At this time, since the receiving apparatus knows that the virtual information bit (120) is “0”, the transmitting apparatus does not transmit the virtual information bit (120) but is generated by the virtual information bit (120). Only the parity bit (130) is transmitted (this parity bit becomes a redundant bit to be transmitted. Therefore, this parity bit is called a redundant bit). Then, as a new problem, in order to achieve both improvement in data transmission efficiency and ensuring of data reception quality, parity bits (120) generated by virtual information bits (120) while ensuring data reception quality. 130) should be as small as possible.

  At this time, in order to reduce the number of parity bits generated by virtual information bits as much as possible while ensuring the reception quality of the data, the terms related to the parity of the parity check polynomial play an important role. It was confirmed by simulation.

ただし、ｉ＝０、１、・・・、ｍ−１とする。また、Ａ_Ｘ１，ｉ（Ｄ）に存在するＤの次数は０以上の整数しか存在せず（例えば、Ａ_Ｘ１，１（Ｄ）＝Ｄ^１５＋Ｄ^３＋Ｄ^０のように、Ｄについて存在する次数は１５、３、０のように、全てが０以上の次数で構成される）、Ｂ_ｉ（Ｄ）に存在するＤの次数も０以上の次数しか存在しないものとする（例えば、Ｂ_ｉ（Ｄ）＝Ｄ^１８＋Ｄ^４＋Ｄ^０のように、Ｄについて存在する次数は１８、４、０のように、全てが０以上の次数で構成される）。 As an example, LDPC-CC when the time varying period m (m is an integer and m ≧ 2) and the coding rate is ½ will be described as an example. When the time-varying period is m, the required m parity check polynomials are expressed by the following equations.

However, i = 0, 1,..., M−1. Further, the order of D existing in A _{X1, i} (D) is only an integer greater than or equal to 0 (for example, the order existing in D such as A _X1,1 (D) = D ¹⁵ + D ³ + D ⁰ ). Are all composed of orders of 0 or more, such as 15, 3, 0), and the order of D existing in B _i (D) also has only orders of 0 or more (for example, B _i ( (D) = D ¹⁸ + D ⁴ + D ⁰ , the orders that exist for D are all composed of orders of 0 or more, such as ^{18, 4} , 0).

At this time, the following parity check polynomial is established at time j.

Then, in X ₁ (D), when the highest order of D in A _X1,1 (D) is α ₁ (for example, A _X1,1 (D) = D ¹⁵ + D ³ + D ⁰ , the order of D is 15, The order 3 and the order 0 exist, and the highest order α _{1 of} D is α ₁ = 15.) The highest order of D in A _X1,2 (D) is α ₂ ,..., A _{X1, i} (D ) Is the highest order of D in α ₎ ,..., A _{X1, m−1} The highest order of D in (D) is α _m−1 . In α _i (i = 0, 1, 2,..., M−1), the largest value is α.

On the other hand, in P (D), the highest order of D in B ₁ (D) is β ₁ , the highest order of D in B ₂ (D) is β ₂ ,..., D in B _i (D) The highest order of β _i ,..., B _m−1 (D) is the highest order of D in β _m−1 . In β _i (i = 0, 1, 2,..., M−1), the largest value is β.

  Then, in order to reduce the number of parity bits generated by the virtual information bits as much as possible while ensuring the reception quality of data, β is preferably set to ½ or less of α.

  Here, the case of a coding rate of ½ has been described, but the case of a coding rate higher than that can also be considered. At this time, particularly in the case of a coding rate of 4/5 or more, redundancy necessary for satisfying the condition that the number of parity bits generated by virtual information bits is as small as possible while ensuring the reception quality of data. Bits tend to be very large, and the conditions considered in the same way as above are to reduce the number of parity bits generated by virtual information bits as much as possible while ensuring the data reception quality It becomes important.

ただし、ｉ＝０、１、・・・、ｍ−１とする。また、Ａ_Ｘ１，ｉ（Ｄ）に存在するＤの次数は０以上の整数しか存在せず（例えば、Ａ_Ｘ１，１（Ｄ）＝Ｄ^１５＋Ｄ^３＋Ｄ^０のように、Ｄについて存在する次数は１５、３、０のように、全てが０以上の次数で構成される）、同様に、Ａ_Ｘ２，ｉ（Ｄ）に存在するＤの次数は０以上の整数しか存在せず、Ａ_Ｘ３，ｉ（Ｄ）に存在するＤの次数は０以上の整数しか存在せず、Ａ_Ｘ４，ｉ（Ｄ）に存在するＤの次数は０以上の整数しか存在せず、Ｂ_ｉ（Ｄ）に存在するＤの次数も０以上の次数しか存在しないものとする（例えば、Ｂ_ｉ（Ｄ）＝Ｄ^１８＋Ｄ^４＋Ｄ^０のように、Ｄについて存在する次数は１８、４、０のように、全てが０以上の次数で構成される）。 As an example, LDPC-CC when the time-varying period m (m is an integer and m ≧ 2) and the coding rate is 4/5 will be described as an example. When the time-varying period is m, the required m parity check polynomials are expressed by the following equations.

However, i = 0, 1,..., M−1. Further, the order of D existing in A _{X1, i} (D) is only an integer greater than or equal to 0 (for example, the order existing in D such as A _X1,1 (D) = D ¹⁵ + D ³ + D ⁰ ). Are all composed of orders of 0 or more, such as 15, 3, 0). Similarly, the order of D existing in A _{X2, i} (D) is only an integer of 0 or more, and A _{X3 , I} (D), the order of D exists only as an integer greater than or equal to 0, the order of D present in A _{X4, i} (D) exists as an integer equal to or greater than 0, and B _i (D) Assume that the order of D that exists is only 0 or more (for example, B _i (D) = D ¹⁸ + D ⁴ + D ⁰ , the orders that exist for D are ^{18, 4, 0} , All are composed of orders of 0 or more).

At this time, the following parity check polynomial is established at time j.

Then, in X ₁ (D), if the highest order of D in A _X1,1 (D) is α _1,1 (for example, A _X1,1 (D) = D ¹⁵ + D ³ + D ⁰ , the order of D 15, order 3, order 0 exists, and D has the highest order α _1,1 = 15.), A _X1,2 (D) has the highest order of D as α _{1,2 ,.} The highest order of D in A _{X1, i} (D) is α _{1, i} ,..., And the highest order of D in A _{X1, m−1} (D) is α _{1, m−1} . In α _{1, i} (i = 0, 1, 2,..., M−1), the largest value is α ₁ .

In X ₂ (D), when the highest order of D in A _X2,1 (D) is α _2,1 (for example, A _X2,1 (D) = D ¹⁵ + D ³ + D ⁰ , the order of D is 15, The order 3 and the order 0 exist, and the highest order α _2,1 = 15 of D.), and the highest order of D in A _X2,2 (D) is represented by α _2,2 ,..., A _{X2 , I} (D), the highest order of D is α _{2, i} ,..., A _{X2, m−1} , and the highest order of D is α _{2, m−1} . In α _{2, i} (i = 0, 1, 2,..., M−1), the largest value is α ₂ .

In X ₃ (D), if the highest order of D in A _X3,1 (D) is α _3,1 (for example, A _X3,1 (D) = D ¹⁵ + D ³ + D ⁰ , then the order of 15 for D, The order 3 and the order 0 exist, and the highest order α _3,1 = 15 of D.), and the highest order of D in A _X3,2 (D) is represented by α _{3,2 ,. , I} (D), the highest order of D is α _{3, i} ,..., A _{X3, m−1} , and the highest order of D is α _{3, m−1} . Then, the largest value in α _{3, i} (i = 0, 1, 2,..., M−1) is α ₃ .

In X ₄ (D), when the highest order of D in A _X4,1 (D) is α _4,1 (for example, A _X4,1 (D) = D ¹⁵ + D ³ + D ⁰ , the order of 15 for D, The order 3 and the order 0 exist, and the highest order α _4,1 = 15 of D.), and the highest order of D in A _X4,2 (D) is α _4,2 ,..., A _{X4 , I} (D), the highest order of D is α _{4, i} ,..., A _{X4, m−1} , and the highest order of D is α _{4, m−1} . In α _{4, i} (i = 0, 1, 2,..., M−1), the largest value is α ₄ .

In P (D), the highest order of D in B ₁ (D) is β ₁ , the highest order of D in B ₂ (D) is β ₂ ,..., B _i (D) is the highest in D The order is β _i ,..., B _m−1 (D), and the highest order of D is β _m−1 . In β _i (i = 0, 1, 2,..., M−1), the largest value is β.

Then, in order to minimize the number of parity bits generated by virtual information bits while ensuring the reception quality of data,
“Β is 1/2 or less of α ₁ , β is 1/2 or less of α ₂ , β is 1/2 or less of α ₃ , and β is 1/2 or less of α ₄ ”
In particular, there is a high possibility that good data reception quality can be secured.

Also,
“Β is 1/2 or less of α ₁ or β is 1/2 or less of α ₂ or β is 1/2 or less of α ₃ or β is 1/2 or less of α ₄ ”
However, while ensuring the data reception quality, the number of parity bits generated by the virtual information bits can be reduced as much as possible, but there is a possibility that the data reception quality will be slightly reduced (however, However, this does not necessarily lead to a decrease in data reception quality.)

  Therefore, in the case of LDPC-CC when the time-varying period m (m is an integer and m ≧ 2) and the coding rate is (n−1) / n, it can be considered as follows.

ただし、ｉ＝０、１、・・・、ｍ−１とする。また、Ａ_Ｘ１，ｉ（Ｄ）に存在するＤの次数は０以上の整数しか存在せず（例えば、Ａ_Ｘ１，１（Ｄ）＝Ｄ^１５＋Ｄ^３＋Ｄ^０のように、Ｄについて存在する次数は１５、３、０のように、全てが０以上の次数で構成される）、同様に、Ａ_Ｘ２，ｉ（Ｄ）に存在するＤの次数は０以上の整数しか存在せず、Ａ_Ｘ３，ｉ（Ｄ）に存在するＤの次数は０以上の整数しか存在せず、Ａ_Ｘ４，ｉ（Ｄ）に存在するＤの次数は０以上の整数しか存在せず、・・・、Ａ_Ｘｕ，ｉ（Ｄ）に存在するＤの次数は０以上の整数しか存在せず、・・・、Ａ_{Ｘｎ−１，ｉ}（Ｄ）に存在するＤの次数は０以上の整数しか存在せず、Ｂ_ｉ（Ｄ）に存在するＤの次数も０以上の次数しか存在しないものとする（例えば、Ｂ_ｉ（Ｄ）＝Ｄ^１８＋Ｄ^４＋Ｄ^０のように、Ｄについて存在する次数は１８、４、０のように、全てが０以上の次数で構成される）（ｕ＝１、２、３、・・・、ｎ−２、ｎ−１）。 When the time-varying period is m, the required m parity check polynomials are expressed by the following equations.

However, i = 0, 1,..., M−1. Further, the order of D existing in A _{X1, i} (D) is only an integer greater than or equal to 0 (for example, the order existing in D such as A _X1,1 (D) = D ¹⁵ + D ³ + D ⁰ ). Are all composed of orders of 0 or more, such as 15, 3, 0). Similarly, the order of D existing in A _{X2, i} (D) is only an integer of 0 or more, and A _{X3 , I} (D), the order of D exists only as an integer greater than or equal to 0, and the order of D present in A _{X4, i} (D) exists only as an integer greater than 0,..., A _{Xu , I} (D), the order of D exists only as an integer greater than or equal to 0,..., A _{Xn-1, i} (D) exists as an order of D as an integer equal to or greater than 0, It is assumed that the order of D existing in B _i (D) also has only an order of 0 or more (for example, B _i (D) = D ¹⁸ + D ⁴ + D ⁰ Thus, the orders existing for D are all composed of orders of 0 or more, such as 18, 4, 0) (u = 1, 2, 3,..., N−2, n−1). .

  At this time, the following parity check polynomial is established at time j.

Then, in X ₁ (D), if the highest order of D in A _X1,1 (D) is α _1,1 (for example, A _X1,1 (D) = D ¹⁵ + D ³ + D ⁰ , the order of D 15, order 3, order 0 exists, and D has the highest order α _1,1 = 15.), A _X1,2 (D) has the highest order of D as α _{1,2 ,.} The highest order of D in A _{X1, i} (D) is α _{1, i} ,..., And the highest order of D in A _{X1, m−1} (D) is α _{1, m−1} . In α _{1, i} (i = 0, 1, 2,..., M−1), the largest value is α ₁ .

In X ₂ (D), when the highest order of D in A _X2,1 (D) is α _2,1 (for example, A _X2,1 (D) = D ¹⁵ + D ³ + D ⁰ , the order of D is 15, The order 3 and the order 0 exist, and the highest order α _2,1 = 15 of D.), and the highest order of D in A _X2,2 (D) is represented by α _2,2 ,..., A _{X2 , I} (D), the highest order of D is α _{2, i} ,..., A _{X2, m−1} , and the highest order of D is α _{2, m−1} . In α _{2, i} (i = 0, 1, 2,..., M−1), the largest value is α ₂ .
・
・
・

In X _u (D), if the highest order of D in A _{Xu, 1} (D) is α _{u, 1} (for example, A _{Xu, 1} (D) = D ¹⁵ + D ³ + D ⁰ , then degree 15 for D, A degree 3 and an order 0 exist, and the highest order α _{u, 1} = 15 of D.), and the highest order of D in A _{Xu, 2} (D) is denoted by α _{u, 2 ,. , I} (D), the highest order of D is α _{u, i} ,..., A _{Xu, m−1} , and the highest order of D is α _{u, m−1} . Then, the largest value in α _{u, i} (i = 0, 1, 2,..., M−1) is α _u . (U = 1, 2, 3,..., N−2, n−1)
・
・
・

In X _n-1 (D), the highest order of D in A _Xn-1,1 (D) is α _n-1,1 (for example, A _Xn-1,1 (D) = D ¹⁵ + D ³ + D ⁰ Then, there is an order 15, an order 3, and an order 0 for D, and the highest order α _n−1,1 = 15 of D.), the highest order of D in A _Xn−1,2 (D) , Α _n−1 ,..., A _{Xn−1, i} (D) is the highest order of D. α _{n−1, i} ,..., A _{Xn−1, m−1} (D) _Let α _{n−1, m−1} be the highest order of D at. Then, the largest value of α _{n−1 , i} (i = 0, 1, 2,..., M−1) is α _n−1 .

In P (D), the highest order of D in B ₁ (D) is β ₁ , the highest order of D in B ₂ (D) is β ₂ ,..., B _i (D) is the highest in D The order is β _i ,..., B _m−1 (D), and the highest order of D is β _m−1 . In β _i (i = 0, 1, 2,..., M−1), the largest value is β.

Then, in order to minimize the number of parity bits generated by virtual information bits while ensuring the reception quality of data,
“Β is ½ or less of α ₁ , β is ½ or less of α ₂ , and..., And β is ½ or less of α _u , and. Is 1/2 or less of α _n−1 (u = 1, 2, 3,..., N−2, n−1) ”
In particular, there is a high possibility that good data reception quality can be secured.

Also,
“Β is 1/2 or less of α ₁ , or β is 1/2 or less of α ₂ , or..., Or β is 1/2 or less of α _u , or. Is 1/2 or less of α _n−1 (u = 1, 2, 3,..., N−2, n−1) ”
However, while ensuring the data reception quality, the number of parity bits generated by the virtual information bits can be reduced as much as possible, but there is a possibility that the data reception quality will be slightly reduced (however, However, this does not necessarily lead to a decrease in data reception quality.)

  Table 6 shows LDPC-CCs with a time-varying period of 3, a coding rate of 1/2, 2/3, 3/4, and 4/5 that can reduce the number of redundant bits while ensuring data reception quality. An example of a parity check polynomial is shown. In the LDPC-CC with time varying period 3 in Table 6, the LDPC-CC with time varying period 3 of two different coding rates out of coding rates 1/2, 2/3, 3/4, and 4/5. When selected, it is verified whether or not a condition that allows the common use of the encoder and decoder described above is verified. In any selection pattern, the same as the LDPC-CC of time varying period 3 in Table 5 In addition, it can be confirmed that the condition that the encoder and the decoder can be shared is satisfied.

  It should be noted that at the coding rate of 5/6 in Table 5, 1000 or more redundant bits were necessary, but at the coding rate of 4/5 in Table 6, it was confirmed that the redundant bits would be 500 bits or less. ing.

Further, in the codes of Table 6, there are different numbers of redundant bits (redundant bits added for “Information-zero-termination”) for each coding rate. At this time, the number of redundant bits tends to increase as the coding rate increases. However, this is not necessarily the case. Also, if the coding rate is large and the information size is large, the number of redundant bits tends to increase. That is, when codes are created as shown in Table 5 and Table 6, when codes of coding rate (n-1) / n and codes of coding rate (m-1) / m exist (n> m) , The number of redundant bits (redundant bits added for “Information-zero-termination”) necessary for the code of the coding rate (n−1) / n is the coding rate (m−1) / m. It tends to be more than the number of redundant bits required for the code (redundant bits added for “Information-zero-termination”), and the redundancy required for the code of coding rate (n−1) / n When the information size is small, the number of bits tends to be larger than the number of redundant bits necessary for a code having a coding rate (m−1) / m. However, this is not necessarily the case.

  As described above, the maximum coding rate is (q-1) / q among the coding rates for the common use of the encoder circuit and the common use of the decoder circuit, and the coding rate (r- 1) An LDPC-CC parity check polynomial with a time varying period g of r / r (r = 2, 3,..., Q (q is a natural number of 3 or more)) has been described (g is an integer of 2 or more).

  Here, at least an LDPC-CC encoder with a time-varying period g of a coding rate (y-1) / y and an LDPC-CC encoder with a time-varying period g of a coding rate (z-1) / z are provided. A transmission device (y ≠ z), an LDPC-CC having at least a coding rate (y−1) / y with a time varying period g, and an LDPC-CC having a coding rate (z−1) / z with a time varying period g. The reception apparatus including the decoder, the method of generating the parity check polynomial of the LDPC-CC having the time-varying period g capable of reducing the operation scale (circuit scale), and the characteristics of the parity check polynomial have been described.

  Here, the transmission apparatus transmits a modulation signal for transmitting an LDPC-CC encoded sequence having a time-varying period g of at least a coding rate (y-1) / y, or a coding rate (z-1) / This is a transmitter capable of generating any one of the modulation signals for transmitting an LDPC-CC encoded sequence having a time-varying period g of z.

  Further, the receiving apparatus receives at least a received signal including an LDPC-CC encoded sequence having a time-varying period g of encoding rate (y-1) / y, or encoding rate (z-1) / z. This is a receiving apparatus that demodulates and decodes any received signal including an LDPC-CC encoded sequence having a variable period g.

  By using the LDPC-CC with the time-varying period g proposed in the present invention, it is possible to reduce the operation scale (circuit scale) between the transmission apparatus equipped with the encoder and the reception apparatus equipped with the decoder ( The circuit can be shared).

  Further, by using the LDPC-CC with the time-varying period g proposed in the present invention, the receiving apparatus has an effect that it can obtain high data reception quality at any coding rate. The configuration of the encoder, the configuration of the decoder, and the operation thereof will be described in detail below.

  Further, in the equations (30-1) to (30- (q-1)), the coding rate is 1/2, 2/3, 3/4, ..., (q-1) / q. The LDPC-CC having the time-varying period g has been described. However, the transmission apparatus having the encoder and the reception apparatus having the decoder have the coding rates 1/2, 2/3, 3/4,. It is not necessary to support all of (q-1) / q, and if at least two different coding rates are supported, the computation scale (circuit scale) of the transmission apparatus and the reception apparatus is reduced (encoding And a common circuit of the decoder and the decoder) and an effect that the receiving apparatus can obtain high data reception quality.

  Further, when all the coding rates supported by the transmission / reception apparatus (encoder / decoder) are codes based on the method described in the present embodiment, the highest coding rate among the supported coding rates. By having a rate encoder / decoder, it is possible to easily cope with encoding and decoding of all coding rates, and at this time, the effect of reducing the operation scale is very large.

  In this embodiment, the description has been made based on the reference numeral (LDPC-CC having good characteristics) described in Embodiment 1, but it is not necessarily described using the above-mentioned (LDPC-CC having good characteristics). If the LDPC-CC has a time-varying period g based on the parity check polynomial in the format described in (LDPC-CC having good characteristics) described above, the present embodiment is similarly implemented. (G is an integer of 2 or more). This is clear from the relationship between (31-1) to (31-g) and (32-1) to (32-g).

  Of course, for example, the transmission / reception apparatus (encoder / decoder) supports coding rates 1/2, 2/3, 3/4, 5/6, and coding rates 1/2, When 2/3 and 3/4 use LDPC-CC based on the above rule, and the code rate 5/6 uses a code not based on the above rule, an encoder / decoder The circuit can be shared for coding rates 1/2, 2/3, and 3/4, and the circuit sharing is difficult for coding rates 5/6.

(Embodiment 3)
In the present embodiment, an LDPC-CC encoder circuit sharing method and a decoder circuit sharing method formed by using the search method described in Embodiment 2 will be described in detail.

  First, according to the present invention, the highest coding rate among the coding rates for the common use of the encoder circuit and the common use of the decoder circuit is (q-1) / q (for example, When the encoding rate corresponding to the transmission / reception apparatus is 1/2, 2/3, 3/4, 5/6, the codes of the encoding rates 1/2, 2/3, and 3/4 are encoded by the encoder / It is assumed that the circuit is shared in the decoder and the coding rate of 5/6 is not the circuit to be shared in the encoder / decoder, in which case the highest coding rate (q− 1) / q is 3/4.), LDPC having a time-varying period g (g is a natural number) that can correspond to a plurality of coding rates (r-1) / r (r is an integer of 2 or more and q or less). A description will be given of an encoder that creates CC.

  FIG. 11 is a block diagram showing an example of a main configuration of the encoder according to the present embodiment. Note that the encoder 200 shown in FIG. 11 is an encoder that can handle coding rates of 1/2, 2/3, and 3/4. 11 includes an information generation unit 210, a first information calculation unit 220-1, a second information calculation unit 220-2, a third information calculation unit 220-3, a parity calculation unit 230, an addition unit 240, It mainly includes a coding rate setting unit 250 and a weight control unit 260.

The information generation unit 210 sets the information X _{1, i} , the information X _{2, i} , and the information X _{3, i} at the time point i according to the coding rate specified by the coding rate setting unit 250. For example, when the coding rate setting unit 250 sets the coding rate to ½, the information generation unit 210 sets the input information data S _j to the information X _{1, i} at the time point i, and the information X at the time point i. _2, the information of _i and time i _{X 3, i} is set to 0.

When the coding rate is 2/3, the information generation unit 210 sets the input information data S _j to the information X _{1, i} at the time point i, and the input information data S _{j + 1} to the information X _{2, i} at the time point i. Set, and set the information X _{3, i} at time i to 0.

When the coding rate is 3/4, the information generation unit 210 sets the input information data S _j to the information X _{1, i} at the time point i, and the input information data S _{j + 1} to the information X _{2, i} at the time point i. Then, the input information data S _{j + 2} is set to the information X _{3, i} at the time point i.

In this manner, the information generating unit 210 according to the coding rate coding rate set by the setting unit 250, information X ₁ of point in time i to input information _{data, i,} information X _{2, i,} information X _{3 , I} are set, the set information X _{1, i} is output to the first information calculation unit 220-1, and the set information X _{2, i} is output to the second information calculation unit 220-2. Then, the set information X _{3, i} is output to the third information calculation unit 220-3.

The first information calculation unit 220-1 calculates X ₁ (D) according to A _{X1, k} (D) in Expression (30-1). Similarly, the second information calculation unit 220-2 calculates X ₂ (D) according to A _{X2, k} (D) in Expression (30-2). Similarly, the third information calculation unit 220-3 calculates X ₃ (D) according to A _{X3, k} (D) in Expression (30-3).

  At this time, as described in the second embodiment, it is assumed that the coding rate is switched from the conditions satisfied in (31-1) to (31-g) and (32-1) to (32-g). However, it is not necessary to change the configuration of the first information calculation unit 220-1, and similarly, there is no need to change the configuration of the second information calculation unit 220-2. Also, the third information calculation unit 220- It is not necessary to change the configuration of 3.

  Therefore, in the case of supporting a plurality of coding rates, the above operation is performed on the basis of the configuration of the encoder with the highest coding rate among the coding rates that can be shared by the encoder circuit. It is possible to cope with other coding rates. That is, the first information calculation unit 220-1, the second information calculation unit 220-2, and the third information calculation unit 220-3, which are main parts of the encoder, are shared regardless of the coding rate. The LDPC-CC described in Embodiment 2 has the advantage that it can be used. For example, the LDPC-CC shown in Table 5 has an advantage of giving good data reception quality regardless of the coding rate.

  FIG. 12 shows the internal configuration of the first information calculation unit 220-1. 12 includes shift registers 221-1 to 221 -M, weight multipliers 222-0 to 222 -M, and an adder 223.

The shift registers 221-1 to 221 -M are registers for holding X _{1, it} (t = 0,..., M−1), and are held at the timing when the next input is input. Is sent to the shift register on the right and the value output from the shift register on the left is held.

The weight multipliers 222-0 to 222-M switch the value of h ₁ ^(m) to 0 or 1 according to the control signal output from the weight control unit 260.

The adder 223 performs an exclusive OR operation on the outputs of the weight multipliers 222-0 to 222-M, calculates an operation result Y1 _{, i,} and calculates the calculated Y1 _{, i} in FIG. Output to the adder 240.

In addition, since the internal structure of the 2nd information calculating part 220-2 and the 3rd information calculating part 220-3 is the same as that of the 1st information calculating part 220-1, description is abbreviate | omitted. Similar to the first information calculation unit 220-1, the second information calculation unit 220-2 calculates the calculation result Y2 _{, i} and outputs the calculated Y2 _{, i} to the addition unit 240. The third information calculation unit 220-3 calculates the calculation result Y _{3, i} in the same manner as the first information calculation unit 220-1, and the calculated Y _{3, i} is directed to the addition unit 240 in FIG. Output.

The parity calculation unit 230 in FIG. 11 calculates P (D) according to B _k (D) in Expression (30-1) to Expression (30-3).

  FIG. 13 shows an internal configuration of the parity calculation unit 230 of FIG. 13 includes a shift register 231-1 to 231-M, a weight multiplier 232-0 to 232-M, and an adder 233.

The shift registers 231-1 to 231 -M are registers that hold P _i-t (t = 0,..., M−1), and are held at the timing when the next input is input. Is sent to the shift register on the right and the value output from the shift register on the left is held.

Weight multipliers 232-0 to 232-M switch the value of h ₂ ^(m) to 0 or 1 according to the control signal output from weight control section 260.

The adder 233 performs an exclusive OR operation on the outputs of the weight multipliers 232-0 to 232-M, calculates an operation result Z _i, and outputs the calculated Z _i to the adder 240 in FIG. Output.

Referring back to FIG. 11 again, the adding unit 240 performs calculations output from the first information calculating unit 220-1, the second information calculating unit 220-2, the third information calculating unit 220-3, and the parity calculating unit 230. The result Y _{1, i} , Y _{2, i} , Y _{3, i} , Z _i is subjected to an exclusive OR operation to obtain and output a parity P _i at time i. The adder 240 also outputs the parity P _i at time i to the parity calculator 230.

  The coding rate setting unit 250 sets the coding rate of the encoder 200 and outputs the coding rate information to the information generation unit 210.

The weight control unit 260 is based on the parity check matrix corresponding to the equations (30-1) to (30-3) held in the weight control unit 260, and the equations (30-1) to (30-3) The value of h ₁ ^(m) at time i based on the parity check polynomial is sent to the first information calculation unit 220-1, the second information calculation unit 220-2, the third information calculation unit 220-3, and the parity calculation unit 230. Output. Further, the weight control unit 260 sets the value of h ₂ ^{(m) at} the timing to 232 based on the parity check matrix corresponding to the equations (30-1) to (30-3) held in the weight control unit 260. Output to -0 to 232-M.

  FIG. 14 shows another configuration example of the encoder according to the present embodiment. In the encoder of FIG. 14, the same reference numerals as those in FIG. 11 are given to the components common to the encoder of FIG. In the encoder 200 of FIG. 14, the coding rate setting unit 250 converts the coding rate information into a first information calculation unit 220-1, a second information calculation unit 220-2, a third information calculation unit 220-3, And it is different from the encoder 200 of FIG. 11 in that it is output toward the parity calculation unit 230.

When the coding rate is 1/2, the second information calculation unit 220-2 outputs 0 to the addition unit 240 as the calculation result Y2 _{, i} without performing the calculation process. In addition, when the coding rate is 1/2 or 2/3, the third information calculation unit 220-3 does not perform the calculation process and directs 0 to the addition unit 240 as the calculation result Y3 _{, i.} Output.

In the encoder 200 of FIG. 11, the information generation unit 210 sets the information X _{2, i} and the information X _{3, i} at the time point _i to 0 according to the coding rate, whereas FIG. In the encoder 200, the second information calculation unit 220-2 and the third information calculation unit 220-3 stop the calculation process according to the coding rate, and obtain the calculation results Y _{2, i} , Y _{3, i} Since 0 is output, the obtained calculation result is the same as that of the encoder 200 of FIG.

  As described above, in the encoder 200 of FIG. 14, the second information calculation unit 220-2 and the third information calculation unit 220-3 stop the calculation process according to the coding rate. Computational processing can be reduced compared to the generator 200.

  Next, a method of sharing the LDPC-CC decoder circuit described in the second embodiment will be described in detail.

  FIG. 15 is a block diagram showing a main configuration of the decoder according to the present embodiment. Note that the decoder 300 shown in FIG. 15 is a decoder that can handle coding rates of 1/2, 2/3, and 3/4. The decoder 300 of FIG. 14 mainly includes a log likelihood ratio setting unit 310 and a matrix processing calculation unit 320.

  Log-likelihood ratio setting section 310 receives a received log-likelihood ratio and a coding rate calculated by a log-likelihood ratio calculation section (not shown), and is known to the received log-likelihood ratio according to the coding rate. Insert log-likelihood ratio.

For example, when the coding rate is ½, this corresponds to transmitting “0” as X _{2, i} , X _{3, i in} the encoder 200, so the log likelihood ratio setting unit 310 , A fixed log-likelihood ratio corresponding to the known bit “0” is inserted as a log-likelihood ratio of X _{2, i} , X _{3, i} , and the log-likelihood ratio after insertion is directed to the matrix processing operation unit 320 Output. Hereinafter, description will be given with reference to FIG.

As shown in FIG. 16, when the coding rate is 1/2, the log likelihood ratio setting unit 310 receives the received log likelihood ratios LLR _{X1, i} , LLR _Pi corresponding to X _{1, i} and P _i as inputs. To do. Accordingly, the log likelihood ratio setting unit 310 inserts the received log likelihood ratios LLR _{X2, i} , LLR _{3, i} corresponding to X _{2, i} , X _{3, i} . In FIG. 16, the reception log likelihood ratio surrounded by a dotted circle indicates the reception log likelihood ratio LLR _{X2, i} , LLR _{3, i} inserted by the log likelihood ratio setting unit 310. Log likelihood ratio setting section 310 inserts a log likelihood ratio of a fixed value as reception log likelihood ratio LLR _{X2, i} , LLR _{3, i} .

Further, when the coding rate is 2/3, this corresponds to the fact that the encoder 200 is transmitting “0” as X _{3, i} , and therefore the log likelihood ratio setting unit 310 determines the known bit “0”. Is inserted as a log likelihood ratio of X _{3, i} , and the log likelihood ratio after the insertion is output to the matrix processing operation unit 320. Hereinafter, a description will be given with reference to FIG.

As shown in FIG. 17, when the coding rate 2/3, log likelihood ratio setting section _{310, X 1, i, X 2} , i and _{P i} corresponding to the received log-likelihood ratio _{LLR X1,} i, LLR _{X2, i} and LLR _Pi are input. Therefore, log likelihood ratio setting section 310 inserts received log likelihood ratio LLR _{3, i} corresponding to X _{3, i} . In FIG. 17, the reception log likelihood ratio surrounded by a dotted circle represents the reception log likelihood ratio LLR _{3, i} inserted by the log likelihood ratio setting unit 310. Log-likelihood ratio setting section 310 inserts a log-likelihood ratio of a fixed value as reception log-likelihood ratio LLR _{3, i} .

  The matrix processing calculation unit 320 of FIG. 15 includes a storage unit 321, a row processing calculation unit 322, and a column processing calculation unit 323.

The storage unit 321 holds the reception log likelihood ratio, the external value α _mn obtained by row processing, and the prior value β _mn obtained by column processing.

The row processing calculation unit 322 holds the weight pattern in the row direction of the parity check matrix H of the LDPC-CC having the maximum coding rate 3/4 among the coding rates supported by the encoder 200. The row processing calculation unit 322 reads the necessary prior value β _mn from the storage unit 321 according to the weight pattern in the row direction, and performs row processing calculation.

In row processing computation, row processing computation section 322, using a priori value beta _mn, it performs decoding of a single parity check codes, obtains external value alpha _mn.

ここで、Φ（ｘ）は、Ｇａｌｌａｇｅｒのｆ関数と呼ばれ、次式で定義される。

The mth row process will be described. However, it is assumed that the binary M × N matrix H = {H _mn } is a parity check matrix of an LDPC code having a decoding target. For all the pairs (m, n) satisfying H _mn = 1, the external value α _mn is updated using the following update formula.

Here, Φ (x) is called Gallager's f function and is defined by the following equation.

The column processing operation unit 323 holds a weight pattern in the column direction of the parity check matrix H of the LDPC-CC having the maximum coding rate 3/4 among the coding rates supported by the encoder 200. The column processing calculation unit 323 reads the necessary external value α _mn from the storage unit 321 according to the weight pattern in the column direction, and obtains the prior value β _mn .

In the column processing calculation, the column processing calculation unit 323 obtains the prior value β _mn by iterative decoding using the input log likelihood ratio λ _n and the external value α _mn .

The mth column process will be described.
For all pairs (m, n) that satisfy H _mn = 1, β _mn is updated using the following update formula. However, calculation is performed with α _mn = 0 only when q = 1.

  The decoder 300 obtains a posterior log likelihood ratio by repeating the above-described row processing and column processing a predetermined number of times.

As described above, in the present embodiment, the highest coding rate among the available coding rates is set to (q−1) / q, and the coding rate setting unit 250 sets the coding rate to (s− 1) When set to / s, the information generation unit 210 sets information from the information X _{s, i} to the information X _{q-1, i} to zero. For example, when the corresponding coding rate is 1/2, 2/3, 3/4 (q = 4), the first information calculation unit 220-1 inputs the information X1 _{, i} at the time point i, and the expression The X ₁ (D) term of (30-1) is calculated. Further, second information computing section 220-2 receives the information _{X 2, i} of the point i, and calculates the _X 2 (D) term of formula (30-2). The third information computing section 220-3 receives the information _{X 3, i} at the time i, and calculates the _X 3 (D) term of formula (30-3). In addition, the parity calculation unit 230 receives the parity P _i−1 at the time point i−1 and calculates the P (D) term in the equations (30-1) to (30-3). Further, the adding unit 240 performs exclusive OR of the calculation results of the first information calculation unit 220-1, the second information calculation unit 220-2, and the third information calculation unit 220-3 and the calculation result of the parity calculation unit 230. , The parity P _{i at} time i is obtained.

  According to this configuration, even when LDPC-CCs corresponding to different coding rates are created, the configuration of the information computation unit in this description can be shared, so that a plurality of coding rates can be achieved with a low computation scale. It is possible to provide an LDPC-CC encoder and decoder that can handle the above.

Further, A _{X1, k} (D) to A _{Xq-1, k} (D) satisfy <Condition # 1> to <Condition # 6> and the like described in the above “LDPC-CC having good characteristics”. In such a case, an encoder and a decoder that can handle different coding rates can be provided on a low computation scale, and the receiver can obtain good data reception quality. . However, as described in the second embodiment, the LDPC-CC generation method is not limited to the above-described “LDPC-CC having good characteristics”.

The decoder 300 in FIG. 15 includes a log-likelihood ratio setting unit in a decoder configuration corresponding to the maximum coding rate among coding rates that enable sharing of the decoder circuit. By adding 310, decoding can be performed corresponding to a plurality of coding rates. In addition, the log likelihood ratio setting unit 310, depending on the coding rate, log likelihood corresponding to (q−2) pieces of information from information X _{r, i} at time _i to information X _{q−1, i.} Set the ratio to the default value.

In the above description, the case where the maximum coding rate supported by the encoder 200 is 3/4 has been described. However, the maximum coding rate supported is not limited to this, and the coding rate (q−1 ) / Q (q is an integer equal to or greater than 5), and is applicable (naturally, the maximum coding rate may be 2/3). In this case, the encoder 200 is configured to include first to (q−1) th information calculation units, and the addition unit 240 includes calculation results and parity of the first to (q−1) th information calculation units. the exclusive oR operation result of the arithmetic unit 230 may be so obtained as parity P _i at time i.

  In addition, when all the coding rates supported by the transmission / reception apparatus (encoder / decoder) are codes based on the method described in the above-described second embodiment, among the coding rates supported, By having an encoder / decoder with a high coding rate, it is possible to cope with encoding and decoding at a plurality of coding rates, and at this time, the effect of reducing the operation scale is very large.

  In the above description, sum-product decoding has been described as an example of the decoding method. However, the decoding method is not limited to this, and is described in Non-Patent Document 5 to Non-Patent Document 7, for example, min It can be similarly implemented by using a decoding method (BP decoding) using a message-passing algorithm such as -sum decoding, Normalized BP (Belief Propagation) decoding, Shuffled BP decoding, and Offset BP decoding.

  Next, a description will be given of a mode in which the present invention is applied to a communication apparatus that adaptively switches the coding rate depending on the communication status. In the following, the case where the present invention is applied to a wireless communication device will be described as an example. However, the present invention is not limited to this, and the present invention is not limited to a power line communication (PLC) device, a visible light communication device, or an optical communication device. Is also applicable.

  FIG. 18 shows a configuration of communication apparatus 400 that adaptively switches the coding rate. The coding rate determination unit 410 of the communication device 400 in FIG. 18 receives a reception signal (for example, feedback information transmitted from the communication partner) transmitted from the communication device of the communication partner, and performs reception processing on the received signal. Then, the coding rate determination unit 410 receives information on the communication status with the communication device of the communication partner, for example, information such as a bit error rate, a packet error rate, a frame error rate, and a received electric field strength (for example, feedback information From the information on the communication status with the communication apparatus of the communication partner, the coding rate and the modulation method are determined. Then, the coding rate determination unit 410 outputs the determined coding rate and modulation scheme to the encoder 200 and the modulation unit 420 as control signals.

  The coding rate determination unit 410 uses, for example, a transmission format as shown in FIG. 19 to include the coding rate information in the control information symbol, thereby changing the coding rate used by the encoder 200 to the communication partner's communication. Notify the device. However, although not shown in FIG. 19, it is assumed that the communication partner includes, for example, a known signal (preamble, pilot symbol, reference symbol, etc.) necessary for demodulation and channel estimation.

  In this way, the coding rate determination unit 410 receives the modulated signal transmitted by the communication partner communication device 500 and determines the coding rate of the modulated signal to be transmitted based on the communication status. Adaptively switch the conversion rate. The encoder 200 performs LDPC-CC encoding according to the above-described procedure based on the encoding rate specified by the control signal. Modulation section 420 modulates the encoded sequence using the modulation scheme specified by the control signal.

  FIG. 20 shows a configuration example of a communication apparatus of a communication partner that communicates with the communication apparatus 400. Control information generating section 530 of communication apparatus 500 in FIG. 20 extracts control information from control information symbols included in the baseband signal. The control information symbol includes coding rate information. Control information generation section 530 outputs the extracted coding rate information as a control signal to log likelihood ratio generation section 520 and decoder 300.

  Receiving section 510 obtains a baseband signal by performing processing such as frequency conversion and orthogonal demodulation on the received signal corresponding to the modulated signal transmitted from communication apparatus 400, and obtains the baseband signal to log likelihood ratio generation section 520. Output toward. In addition, the reception unit 510 estimates a channel variation in a (for example, wireless) transmission path between the communication device 400 and the communication device 500 using a known signal included in the baseband signal, and obtains the estimated channel estimation signal. Output to log likelihood ratio generation section 520.

  In addition, the reception unit 510 uses a known signal included in the baseband signal to estimate channel fluctuation in a (for example, wireless) transmission path between the communication apparatus 400 and the communication apparatus 500, and determines the state of the propagation path. Feedback information (channel fluctuation itself, for example, Channel State Information is an example) is generated and output. This feedback information is transmitted to a communication partner (communication device 400) as part of control information through a transmission device (not shown). Log likelihood ratio generation section 520 obtains the log likelihood ratio of each transmission sequence using the baseband signal, and outputs the obtained log likelihood ratio to decoder 300.

As described above, the decoder 300 corresponds to the information from the information X _{s, i} at the time point _i to the information X _{s-1, i} according to the coding rate (s−1) / s indicated by the control signal. BP decoding is performed using an LDPC-CC parity check matrix corresponding to the maximum coding rate among the coding rates obtained by sharing the circuit in the decoder. .

  In this way, the coding rates of the communication device 400 to which the present invention is applied and the communication device 500 of the communication partner can be adaptively changed according to the communication status.

  Note that the coding rate changing method is not limited to this, and the communication apparatus 500 that is the communication partner may include the coding rate determination unit 410 to specify a desired coding rate. Further, the communication apparatus 400 may estimate the fluctuation of the transmission path from the modulated signal transmitted by the communication apparatus 500 and determine the coding rate. In this case, the above feedback information is not necessary.

(Embodiment 4)
In the first embodiment, the LDPC-CC having a high error correction capability has been described. In the present embodiment, a supplementary description will be given of an LDPC-CC with a time-varying period 3 having a high error correction capability. In the case of an LDPC-CC with a time-varying period of 3, when a regular LDPC code is generated, a code with high error correction capability can be created.

  The parity check polynomial of LDPC-CC with time-varying period 3 is shown again.

For coding rate 1/2:

For coding rate (n-1) / n:

  Here, it is assumed that the following conditions are satisfied so that the parity check matrix becomes full rank and the parity bits can be easily obtained sequentially.

b3 = 0, that is, D ^b3 = 1
B3 = 0, that is, D ^B3 = 1
β3 = 0, that is, D ^β3 = 1

In order to make the relationship between information and parity easy to understand, the following conditions should be satisfied.
ai, 3 = 0, that is, D ^{ai, 3} = 1 (i = 1, 2,..., n−1)
Ai, 3 = 0, that is, D ^{Ai, 3} = 1 (i = 1, 2,..., N−1)
αi, 3 = 0, that is, D ^{αi, 3} = 1 (i = 1, 2,..., n−1)
However, ai, 3% 3 = 0, Ai, 3% 3 = 0, αi, 3% 3 = 0 may be used.

  At this time, in order to generate a regular LDPC code having a high error correction capability by reducing the number of loops 6 in the Tanner graph, the following conditions must be satisfied.

That is, when focusing on the coefficient of the information Xk (k = 1, 2,..., N−1), one of # Xk1 to # Xk14 must be satisfied.
# Xk1: (ak, 1% 3, ak, 2% 3) = [0,1], (Ak, 1% 3, Ak, 2% 3) = [0,1], (αk, 1% 3, αk, 2% 3) = [0,1]
# Xk2: (ak, 1% 3, ak, 2% 3) = [0,1], (Ak, 1% 3, Ak, 2% 3) = [0,2], (αk, 1% 3, αk, 2% 3) = [1,2]
# Xk3: (ak, 1% 3, ak, 2% 3) = [0,1], (Ak, 1% 3, Ak, 2% 3) = [1,2], (αk, 1% 3, αk, 2% 3) = [1,1]
# Xk4: (ak, 1% 3, ak, 2% 3) = [0,2], (Ak, 1% 3, Ak, 2% 3) = [1,2], (αk, 1% 3, αk, 2% 3) = [0,1]
# Xk5: (ak, 1% 3, ak, 2% 3) = [0,2], (Ak, 1% 3, Ak, 2% 3) = [0,2], (αk, 1% 3, αk, 2% 3) = [0,2]
# Xk6: (ak, 1% 3, ak, 2% 3) = [0,2], (Ak, 1% 3, Ak, 2% 3) = [2,2], (αk, 1% 3, αk, 2% 3) = [1,2]
# Xk7: (ak, 1% 3, ak, 2% 3) = [1,1], (Ak, 1% 3, Ak, 2% 3) = [0,1], (αk, 1% 3, αk, 2% 3) = [1,2]
# Xk8: (ak, 1% 3, ak, 2% 3) = [1,1], (Ak, 1% 3, Ak, 2% 3) = [1,1], (αk, 1% 3, αk, 2% 3) = [1,1]
# Xk9: (ak, 1% 3, ak, 2% 3) = [1,2], (Ak, 1% 3, Ak, 2% 3) = [0,1], (αk, 1% 3, αk, 2% 3) = [0,2]
# Xk10: (ak, 1% 3, ak, 2% 3) = [1,2], (Ak, 1% 3, Ak, 2% 3) = [0,2], (αk, 1% 3, αk, 2% 3) = [2,2]
# Xk11: (ak, 1% 3, ak, 2% 3) = [1,2], (Ak, 1% 3, Ak, 2% 3) = [1,1], (αk, 1% 3, αk, 2% 3) = [0,1]
# Xk12: (ak, 1% 3, ak, 2% 3) = [1,2], (Ak, 1% 3, Ak, 2% 3) = [1,2], (αk, 1% 3, αk, 2% 3) = [1,2]
# Xk13: (ak, 1% 3, ak, 2% 3) = [2,2], (Ak, 1% 3, Ak, 2% 3) = [1,2], (αk, 1% 3, αk, 2% 3) = [0,2]
# Xk14: (ak, 1% 3, ak, 2% 3) = [2,2], (Ak, 1% 3, Ak, 2% 3) = [2,2], (αk, 1% 3, αk, 2% 3) = [2,2]

  In the above, when a = b, (x, y) = [a, b] represents x = y = a (= b), and when a ≠ b, (x, y) = [a , b] represents x = a, y = b, or x = b, y = a (the same applies hereinafter).

Similarly, when paying attention to the coefficient of parity, one of # P1 to # P14 must be satisfied.
# P1: (b1% 3, b2% 3) = [0,1], (B1% 3, B2% 3) = [0,1], (β1% 3, β2% 3) = [0,1]
# P2: (b1% 3, b2% 3) = [0,1], (B1% 3, B2% 3) = [0,2], (β1% 3, β2% 3) = [1,2]
# P3: (b1% 3, b2% 3) = [0,1], (B1% 3, B2% 3) = [1,2], (β1% 3, β2% 3) = [1,1]
# P4: (b1% 3, b2% 3) = [0,2], (B1% 3, B2% 3) = [1,2], (β1% 3, β2% 3) = [0,1]
# P5: (b1% 3, b2% 3) = [0,2], (B1% 3, B2% 3) = [0,2], (β1% 3, β2% 3) = [0,2]
# P6: (b1% 3, b2% 3) = [0,2], (B1% 3, B2% 3) = [2,2], (β1% 3, β2% 3) = [1,2]
# P7: (b1% 3, b2% 3) = [1,1], (B1% 3, B2% 3) = [0,1], (β1% 3, β2% 3) = [1,2]
# P8: (b1% 3, b2% 3) = [1,1], (B1% 3, B2% 3) = [1,1], (β1% 3, β2% 3) = [1,1]
# P9: (b1% 3, b2% 3) = [1,2], (B1% 3, B2% 3) = [0,1], (β1% 3, β2% 3) = [0,2]
# P10: (b1% 3, b2% 3) = [1,2], (B1% 3, B2% 3) = [0,2], (β1% 3, β2% 3) = [2,2]
# P11: (b1% 3, b2% 3) = [1,2], (B1% 3, B2% 3) = [1,1], (β1% 3, β2% 3) = [0,1]
# P12: (b1% 3, b2% 3) = [1,2], (B1% 3, B2% 3) = [1,2], (β1% 3, β2% 3) = [1,2]
# P13: (b1% 3, b2% 3) = [2,2], (B1% 3, B2% 3) = [1,2], (β1% 3, β2% 3) = [0,2]
# P14: (b1% 3, b2% 3) = [2,2], (B1% 3, B2% 3) = [2,2], (β1% 3, β2% 3) = [2,2]

  The LDPC-CC with good characteristics described in the first embodiment is an LDPC-CC that satisfies the conditions of # Xk12 and # P12 among the above conditions. Further, when used together with the second embodiment, the circuit scales of the encoder and decoder can be reduced and high error correction capability can be obtained when dealing with a plurality of coding rates.

  An example of an LDPC-CC parity check polynomial of time-varying period 3 that satisfies any one of # Xk1 to # Xk14 and any one of # P1 to # P14 is shown below.

Coding rate R = 1/2:

Coding rate R = 2/3:

Coding rate R = 3/4:

Coding rate R = 4/5:

  Since the LDPC-CC parity check polynomial satisfies the conditions described in Embodiment 2, the encoder circuit can be shared and the decoder can be shared.

  By the way, when the parity check polynomial of LDPC-CC shown in Expression (44-i), Expression (45-i), Expression (46-i), and Expression (47-i) is used (i = 1, 2, 3). ), It was confirmed that the necessary number of terminations differs depending on the number of bits of data (information) X (hereinafter referred to as “information size”), as shown in FIG. Here, the number of terminations is the number of parity bits generated by the virtual known information bit “0” after performing the above-described information-zero-termination, and is the number of redundant bits actually transmitted. In FIG. 21, Real R (effective coding rate) indicates a coding rate when a termination sequence composed of redundant bits is considered.

  Another example of the parity check polynomial of the LDPC-CC with time-varying period 3 that satisfies any one of # Xk1 to # Xk14 and any one of # P1 to # P14 is shown below.

Coding rate R = 1/2:

Coding rate R = 2/3:

Coding rate R = 3/4:

Coding rate R = 4/5:

  FIG. 22 shows a case where the parity check polynomial of LDPC-CC shown in Equation (48-i), Equation (49-i), Equation (50-i), and Equation (51-i) is used (i = 1, 2, 3) shows an example of the number of terminations required.

なお、ｋ＝Ｉ_ｓ％（ｎ−１）である。 FIG. 23 shows information (i = 1, 2, 3) at each coding rate represented by the equations (48-i), (49-i), (50-i), and (51-i). It shows the relationship between the size I _s and the termination number m _t. Note that if the number of virtual known information bits (“0”) to be inserted to create a termination sequence is m _z , the coding rate (n−1) / n is between m _t and m _z. The following relationship holds.

Note that k = I _s % (n−1).

(Embodiment 5)
In the present embodiment, when the LDPC-CC having the good characteristics described in the fourth embodiment is used, a communication apparatus capable of avoiding a reduction in information transmission efficiency without deteriorating error correction capability. The communication method will be described.

  From FIG. 21 and FIG. 22, it was confirmed that the number of terminations required at the time of information-zero-termination differs depending on the information size. Therefore, in order to fix the number of terminations uniformly regardless of the information size and not to deteriorate the error correction capability, it is necessary to set the number of terminations to a large number, and the Real R (effective coding rate) decreases. The transmission efficiency of information may be reduced.

  Therefore, in the present embodiment, a communication device and a communication method for changing the number of terminations transmitted as redundant bits according to the information size will be described. As a result, the error correction capability is not deteriorated and a reduction in information transmission efficiency can be avoided.

  FIG. 24 is a block diagram showing a main configuration of communication apparatus 600 according to the present embodiment.

  The coding rate setting unit 610 receives a control information signal including coding rate information set by the own device or a feedback signal transmitted from the communication device of the communication partner. When the control information signal is input, coding rate setting section 610 sets the coding rate from the coding rate information included in the control information signal.

  In addition, when a feedback signal is input, the coding rate setting unit 610 includes information on a communication status with the communication apparatus of the communication partner included in the feedback signal, for example, a bit error rate, a packet error rate, a frame Information capable of estimating communication quality such as an error rate and received electric field strength is acquired, and a coding rate is set from information on a communication state with a communication apparatus as a communication partner. The coding rate setting unit 610 includes information on the set coding rate in the set coding rate signal, and the set coding rate signal is directed to the termination sequence length determination unit 631 and the parity calculation unit 632 in the encoder 630. Output. Also, the coding rate setting unit 610 outputs information on the set coding rate to the transmission information generation and information length detection unit 620.

  The transmission information generation and information length detection unit 620 generates or acquires transmission data (information), and outputs an information sequence including the transmission data (information) to the parity calculation unit 632. The transmission information generation and information length detection unit 620 detects a sequence length of transmission data (information) (hereinafter referred to as “information length”), that is, an information size, and includes information on the detected information size in the information length signal. The information length signal is output to the termination sequence length determination unit 631. The transmission information generation and information length detection unit 620 includes known information bits (for example, “0”) necessary for generating redundant bits for the termination sequence length notified from the termination sequence length determination unit 631. Is added to the end of the information series.

  Termination sequence length determination section 631 determines the termination sequence length (number of terminations) according to the information size indicated by the information length signal and the coding rate indicated by the set coding rate signal. A specific method for determining the termination sequence length will be described later. Termination sequence length determination section 631 includes the determined termination sequence length in the termination sequence length signal, and outputs the termination sequence length signal to transmission information generation and information length detection section 620 and parity calculation section 632.

  The parity calculation unit 632 calculates parity for the information sequence and the known information sequence, and outputs the obtained parity to the modulation unit 640.

  Modulation section 640 performs modulation processing on the information sequence and parity (including termination sequence).

  In FIG. 24, “Information Length signal” is described. However, the present invention is not limited to this, and any signal can be used as long as the information is an index for controlling the termination sequence length. May be. For example, the frame length of the transmission signal is obtained from the information (Length information) of the number of information excluding termination and the number of parity, the information number and the modulation method information, and the frame length can be used instead of the information length signal. Good.

  Next, a termination sequence length determination method in termination sequence length determination section 631 will be described with reference to FIG. FIG. 25 shows an example in which the termination sequence length is switched in two stages based on the information size and each coding rate. FIG. 25 assumes that the minimum information size is set to 512 bits in the communication apparatus 600. However, the minimum size is not necessarily determined.

  In FIG. 25, α is the information length of transmission data (information) that must be transmitted. For example, when the coding rate is 1/2, when 512 ≦ α ≦ 1023, the termination sequence length determination unit 631 sets the termination sequence length to 380 bits, and when 1024 ≦ α, the termination sequence length determination unit 631 Set the termination sequence length to 340 bits. In this way, the termination sequence length determination unit 631 sets the termination sequence length based on the information length α of the transmission data (information), so that the termination sequence length does not deteriorate the error correction capability, and The sequence length is set so as to prevent a decrease in information transmission efficiency.

  In the above description, the case where the termination sequence length is switched to two stages at each coding rate has been described as an example. However, the present invention is not limited to this. For example, three stages or more stages as shown in FIG. The termination sequence length may be switched with. In this way, by switching the termination sequence length (number of terminations) to multiple stages based on the information length (information size), the termination sequence length does not degrade the error correction capability and the information transmission efficiency decreases. It is possible to set a suitable sequence length that can prevent

  The communication device 600 uses the transmission format as shown in FIG. 27, for example, to include the coding rate information in the symbol related to the coding rate, thereby changing the coding rate used by the encoder 630 to the communication device of the communication partner. Notify Further, the communication apparatus 600 notifies the information of the information length (information size) to the communication apparatus of the communication partner by including information of the information length (information size) in the symbol related to the information size. Communication device 600 also includes information for identifying the modulation method, transmission method, or communication partner in the control information symbol, and notifies the communication device of the communication partner. Communication device 600 also includes the information sequence and parity in the data symbol and notifies the communication device of the communication partner.

  FIG. 28 shows a configuration example of communication apparatus 700 of a communication partner that communicates with communication apparatus 600. In the communication apparatus 700 of FIG. 28, the same components as those in FIG. 20 are denoted by the same reference numerals as those in FIG. The communication device 700 in FIG. 28 includes a control information generation unit 710 and a decoder 720 instead of the control information generation unit 530 and the decoder 300 in the communication device 500 in FIG.

  Control information generation section 710 extracts coding rate information from symbols relating to the coding rate obtained by demodulating (and decoding) the baseband signal. Further, the control information generation unit 710 extracts information length (information size) information from symbols related to information size obtained by demodulating (and decoding) the baseband signal. Control information generation section 710 also extracts information for identifying the modulation scheme, transmission method, or communication partner from the control information symbols. The control information generation unit 710 outputs a control signal including the extracted coding rate information and information length (information size) information to the log likelihood ratio generation unit 520 and the decoder 720.

  The decoder 720 holds a table of the relationship between the information size and the termination sequence length at each coding rate as shown in FIG. 25 or 26, and this table, coding rate information, and The termination sequence length included in the data symbol is determined from information on the information length (information size). Decoder 720 performs BP decoding based on the coding rate and the determined termination sequence length. Thereby, the communication apparatus 700 can perform decoding with high error correction capability.

  29 and 30 are diagrams illustrating an example of the flow of information between the communication device 600 and the communication device 700. FIG. FIG. 29 differs from FIG. 30 in whether the coding rate is set by communication apparatus 600 or communication apparatus 700. Specifically, FIG. 29 shows the information flow when the communication apparatus 600 determines the coding rate, and FIG. 30 shows the information flow when the communication apparatus 700 determines the coding rate. .

  As described above, in the present embodiment, termination sequence length determination section 631 determines the sequence length of the termination sequence that is added to the tail of the information sequence and transmitted according to the information length (information size) and coding rate. The parity calculation unit 632 performs LDPC-CC coding on the information sequence and the known information sequence necessary for generating the termination sequence for the determined termination sequence length, and calculates the parity sequence. I made it. As a result, the error correction capability is not deteriorated and a reduction in information transmission efficiency can be avoided.

(Embodiment 6)
In the fifth embodiment, the case where the termination sequence length added to the tail of the information sequence is determined (changed) according to the information length (information size) and the coding rate has been described. As a result, the error correction capability is not deteriorated and a reduction in information transmission efficiency can be avoided.

  In the present embodiment, a case will be described in which the coding rate that can be used is limited when the termination sequence length is changed according to the information length (information size) as in the fifth embodiment. Thereby, it is possible to avoid the deterioration of the error correction capability.

  FIG. 31 shows a case where the parity check polynomial of LDPC-CC shown in Equation (44-i), Equation (45-i), Equation (46-i), and Equation (47-i) is used, as in FIG. The relationship between the number of terminations required for (i = 1, 2, 3) and the coding rate is shown. As can be seen from FIG. 31, when the information size is 512 bits, 1024 bits, and 2048 bits, the effective coding rate (Real R) at the coding rate 3/4 and the effective coding rate at the coding rate 4/5 are obtained. In comparison, there is no significant difference between the two. For example, when the information size is 1024 bits, the effective coding rate is 0.5735 at the coding rate 3/4, whereas the effective coding rate is 0.5626 at the coding rate 4/5, and the difference is slight. Is about 0.01. In addition, the effective coding rate of the coding rate 3/4 is larger than the effective coding rate of the coding rate 4/5, and the size of the effective coding rate is reversed. Therefore, depending on the information size, there are cases where even if the coding rate of 3/4 is used, high error correction capability is obtained and transmission efficiency is not suitable.

  32A, 32B, 32C and 32D show the bit error rates when the termination sequence having the sequence length shown in FIG. 31 is added to an information sequence having an information size of 512 bits, 1024 bits, 2048 bits and 4096 bits. (Bit Error Rate: BER) / Block Error Rate (BLER) characteristics are shown. 32A, 32B, 32C, and 32D, the horizontal axis represents SNR (Signal-to-Noise power ratio) [dB], the vertical axis represents BER / BLER characteristics, the solid line represents bit error rate characteristics, and the broken line. Indicates block error rate characteristics. Further, in FIGS. 32A, 32B, 32C, and 32D, TMN indicates a termination number.

  As can be seen from FIGS. 32A, 32B, 32C, and 32D, when the termination sequence is taken into consideration, the BER / BLER characteristic at the coding rate R = 3/4 has the coding rate R regardless of the information size. It can be seen that this is superior to the BER / BLER characteristic of 4/5.

  From these two points, in order to realize both improvement in error correction capability and improvement in information transmission efficiency, for example, when the information size is less than 4096 bits, the coding rate R = 4/5 is not supported. When the information size is less than 4096 bits, only the coding rate R = 1/2, 2/3, 3/4 is supported, and when the information size is 4096 bits or more, the coding rate R = 1/2, 2/3. , 3/4, 4/5 are supported, and if the information size is less than 4096 bits, a coding rate R = 4/5, which has a lower transmission efficiency than the coding rate R = 3/4, is used. Therefore, it is possible to achieve both improvement in error correction capability and improvement in information transmission efficiency.

  32A, 32B, 32C, and 32D show that the BER / BLER characteristic with an information size of 512 bits (see FIG. 32A) is markedly superior to the BER / BLER characteristic with other information sizes. . For example, when the information size is 512 bits, the coding rate 2/3 BER characteristic is substantially equivalent to the coding rate 1/2 BER / BLER characteristic when the information size is 1024 bits. When the information size is 512 bits, the BER / BLER characteristic with a coding rate of 1/2 may be actually unnecessary. Considering these points, for example, when the information size is 512 bits, it is possible to adopt a method of not supporting the coding rate 1/2, since the lower the coding rate, the lower the propagation efficiency. .

  FIG. 33 is a correspondence table between information sizes and supported coding rates. As shown in FIG. 33, there is an unsupported coding rate depending on the information size. If the supported coding rate is constant regardless of the information size, the communication apparatus 600 and the communication apparatus 700 can communicate with each other in both cases of FIGS. However, as shown in FIG. 33, in the present embodiment, there is an unsupported coding rate depending on the information size, and therefore it is necessary to adjust the designated coding rate. Hereinafter, the communication device according to the present embodiment will be described.

  FIG. 34 is a block diagram showing the main configuration of communication apparatus 600A according to the present embodiment. In the communication apparatus 600A of FIG. 34, the same components as those in FIG. 24 are denoted by the same reference numerals as those in FIG. A communication apparatus 600A in FIG. 34 includes an encoder 630A in place of the encoder 630 in FIG. Encoder 630A employs a configuration in which coding rate adjustment section 633 is added to encoder 630.

  Based on the information length (information size) included in the information length signal input from the transmission information generation and information length detection unit 620, the coding rate adjustment unit 633 performs setting coding input from the coding rate setting unit 610. The coding rate included in the rate signal is adjusted. Specifically, the coding rate adjustment unit 633 holds a correspondence table between the information size and the support coding rate as illustrated in FIG. 33, and is set based on the control information signal or the feedback signal. The coding rate is adjusted with reference to the correspondence table. For example, if the information length (information size) is 1024 bits and the set coding rate signal indicates the coding rate 4/5, the coding rate 4/5 is not supported from the correspondence table. The unit 633 sets 3/4 having the largest value among the coding rates smaller than the coding rate 4/5 as the coding rate. As shown in FIG. 31, when the information length (information size) is 1024 bits, Real R at a coding rate of 4/5 is 0.5626, and Real R (0.5735) at a coding rate of 3/4. Further, as shown in FIG. 32B, the BER / BLER characteristic is better at the coding rate of 3/4. Therefore, when the information length (information size) is 1024, the error correction capability is not deteriorated by using the coding rate 3/4 without using the coding rate 4/5, and the information The transmission efficiency can be prevented from decreasing.

  In other words, when the first coding rate (3/4) <the second coding rate (4/5), the first effective coding corresponding to the first coding rate (3/4). If the second coding rate is designated when the rate (0.5735) is the same as the second effective coding rate (0.5626) corresponding to the second coding rate (4/5), the code The coding rate adjustment unit 633 adjusts the coding rate to the first coding rate. Thereby, it is possible to prevent the error correction capability from being deteriorated and the information transmission efficiency from being lowered.

  For example, when the information length (information size) is 512 bits and the set coding rate signal indicates the coding rate 1/2, the coding rate 1/2 is not supported from the correspondence table. The coding rate adjustment unit 633 sets 2/3 having the smallest value among the coding rates larger than the coding rate 1/2 to the coding rate. As shown in FIG. 32A, since the BER / BLER characteristic at a coding rate of 1/2 is very good, even if the coding rate is 2/3, the error correction capability is not deteriorated and information transmission is performed. The efficiency can be prevented from decreasing.

  In other words, when the first coding rate having a very good BER / BLER characteristic is designated, the coding rate adjusting unit 633 has a coding rate higher than the first coding rate and has a predetermined channel quality. The coding rate is adjusted to the second coding rate that can ensure the above.

  Thus, in the present embodiment, the number of coding rates supported by communication apparatus 600A is changed based on the information length (information size). For example, in the example shown in FIG. 33, if the information length (information size) is less than 512 bits, the communication device 600A supports only two coding rates, and if the information length (information size) is 512 bits or more and less than 4096 bits. Three coding rates are supported, and when the information length (information size) is 4096 or more, four coding rates are supported. By changing the coding rate to be supported, it is possible to achieve both improvement in error correction capability and improvement in information transmission efficiency.

  As described above, according to the present embodiment, coding rate adjustment section 633 changes the number of coding rates supported by communication apparatus 600A according to the information length (information size), and changes the coding rate. Adjusted to one of the supported coding rates. Thereby, it is possible to prevent the error correction capability from being deteriorated and the information transmission efficiency from being lowered.

  Further, the communication device 600A supports a coding rate having a small value among coding rates having the same effective coding rate. The communication device 600A supports only a coding rate that can ensure a predetermined line quality, without being included in a coding rate that supports a coding rate with very good BER / BLER characteristics. Thereby, it is possible to avoid a decrease in transmission efficiency while ensuring a predetermined line quality.

  As described above, by changing the number of coding rates to be supported according to the information length (information size), it is possible to achieve both improvement in error correction capability and improvement in information transmission efficiency.

  When changing the number of supported coding rates according to the information length (information size), as shown in FIG. 29, the communication apparatus 600A adjusts the coding rate and sets the termination sequence length. If the coding rate information and the information length (information size) information (or termination sequence length information) are simultaneously transmitted to the communication device 700 of the communication partner, the communication device 700 can correctly decode.

  Of course, this embodiment may be used in combination with the fifth embodiment. That is, the number of terminations may be changed depending on the coding rate and the information size.

  On the other hand, as shown in FIG. 30, before the communication device 600A determines the information length (information size), the communication device of the communication partner of the communication device 600 sets the coding rate, or as shown in FIG. As described above, when the communication apparatus 600A sets the coding rate before the communication apparatus 600A determines the information length (information size), the communication apparatus of the communication partner of the communication apparatus 600A is based on the information length (information size). Therefore, it is necessary to adjust the coding rate. FIG. 36 is a block diagram showing a configuration of communication apparatus 700A in this case.

  In the communication apparatus 700A of FIG. 36, the same reference numerals as those in FIG. 36 employs a configuration in which a coding rate adjustment unit 730 is added to communication apparatus 700 in FIG.

  In the following, the communication device 600A supports coding rates 1/2, 2/3, and 3/4 when the information length (information size) is less than 4096 bits, and the code length is 4097 bits when the information length (information size) is 4097 bits. A case of supporting the conversion ratios 1/2, 2/3, 3/4, and 4/5 will be described.

  At this time, before the information length (information size) is determined, the coding rate of the information sequence to be transmitted is determined to be 4/5, and the communication device 600A and the communication device 700A share this coding rate information. It shall be. When the information length (information size) is 512 bits, as described above, the coding rate adjustment unit 633 of the communication device 600A adjusts the coding rate to 3/4. If this rule is determined in advance between communication device 600A and communication device 700A, communication device 600A and communication device 700A can communicate correctly.

  Specifically, as with the coding rate adjustment unit 633, the coding rate adjustment unit 730 receives a control signal including coding rate information and information length (information size) information as an information length (information The coding rate is adjusted based on the size. For example, when the information length (information size) is 512 bits and the coding rate is 4/5, the coding rate adjustment unit 730 adjusts the coding rate to 3/4. . Thereby, it is possible to prevent the error correction capability from being deteriorated and the information transmission efficiency from being lowered.

  As another coding rate adjustment method, a method of making the number of terminations constant irrespective of the coding rate is also conceivable. In the example of FIG. 21, when the information length (information size) is 6144 or more, the number of terminations is uniform at 340 bits. Therefore, when the information length (information size) is 6144 bits or more, the coding rate adjustment unit 633 and the coding rate adjustment unit 730 may make the number of terminations constant regardless of the coding rate. . In addition, when the information length (information size) is less than 6144, the coding rate adjustment unit 633 and the coding rate adjustment unit 730 use, for example, another parity check polynomial suitable for a termination number of 340 bits, You may make it respond | correspond to a code rate. A completely different code may be used. For example, a block code may be used.

(Embodiment 7)
In each of the above-described embodiments, the LDPC-CC has been described in which a circuit corresponding to a plurality of coding rates of coding rate ½ or more can be shared in the encoder / decoder. Specifically, an LDPC-CC that can be used in common with a coding rate (n−1) / n (n = 2, 3, 4, 5) that can share a circuit has been described. In the present embodiment, a method for dealing with a coding rate of 1/3 will be described.

  FIG. 37 is a block diagram showing an example of the configuration of the encoder according to the present embodiment. In the encoder 800 of FIG. 37, the coding rate setting unit 810 outputs the coding rate to the control unit 820, the parity calculation unit 830, and the parity calculation unit 840.

  The control unit 820 performs control so that information is not input to the parity calculation unit 840 when the coding rate setting unit 810 designates coding rates 1/2, 2/3, 3/4, and 4/5. Also, the control unit 820 performs control so that the same information as the information input to the parity calculation unit 830 is input to the parity calculation unit 840 when the coding rate 1/3 is set.

  The parity calculation unit 830 is defined by, for example, Expression (44-i), Expression (45-i), Expression (46-i), Expression (47-i) (i = 1, 2, 3), It is an encoder that obtains parity of conversion rates 1/2, 2/3, 3/4, and 4/5.

  When the coding rate setting unit 810 designates coding rates 1/2, 2/3, 3/4, and 4/5, the parity calculation unit 830 performs coding based on the corresponding parity check polynomial. , Output parity.

  When the coding rate setting unit 810 specifies the coding rate 1/3, the parity calculation unit 830 calculates the coding rate 1/2 (formula (44-1), formula (44-2), formula (4)). 44-3) is performed based on the LDPC-CC parity check polynomial of time-varying period 3), and parity P is output.

  The parity calculation unit 840 is an encoder that calculates parity with a coding rate of 1/2. When the coding rate setting unit 810 designates coding rates 1/2, 2/3, 3/4, and 4/5, the parity calculation unit 840 does not output parity.

  When the coding rate setting unit 810 designates the coding rate 1/3, the parity calculation unit 840 receives the same information as the information input to the parity calculation unit 830 and inputs the coding rate 1/2. Encoding based on the parity check polynomial of the LDPC-CC with the time varying period 3 is performed, and the parity Pa is output.

  In this way, the encoder 800 outputs information, parity P, and parity Pa, so that the encoder 800 can support a coding rate of 1/3.

  FIG. 38 is a block diagram showing an example of the configuration of the decoder according to the present embodiment. The decoder 900 in FIG. 38 is a decoder corresponding to the encoder 800 in FIG.

  The control unit 910 receives the coding rate information indicating the coding rate and the log likelihood ratio as input, and when the coding rate is 1/2, 2/3, 3/4, 4/5, the control unit 910 transmits the coding rate information to the BP decoding unit 930. Control is performed so that the log likelihood ratio is not input. In addition, when the coding rate is 1/3, the control unit 910 performs control so that the same log likelihood ratio as the log likelihood ratio input to the BP decoding unit 920 is input to the BP decoding unit 930.

  The BP decoding unit 920 operates at all coding rates. Specifically, when the coding rate is 1/3, the BP decoding unit 920 performs BP decoding using the parity check polynomial of the coding rate 1/2 used in the parity calculation unit 830. When the coding rate is 1/3, the BP decoding unit 920 outputs a log likelihood ratio corresponding to each bit obtained by performing BP decoding to the BP decoding unit 930. On the other hand, when the coding rate is 1/2, 2/3, 3/4, 4/5, the BP decoding unit 920 uses the coding rate 1/2, 2/3, 3 used in the parity calculation unit 830. BP decoding is performed using a parity check polynomial of / 4, 4/5. The BP decoding unit 920 performs iterative decoding a predetermined number of times, and then outputs the obtained log likelihood ratio.

  The BP decoding unit 930 operates only when the coding rate is 1/3. Specifically, the BP decoding unit 930 performs BP decoding using the parity check polynomial with a coding rate of ½ used in the parity calculation unit 840 and applies each bit obtained by performing BP decoding. The corresponding log likelihood ratio is output to the BP decoding unit 920, and after iterative decoding is performed a predetermined number of times, the obtained log likelihood ratio is output.

  In this way, the decoder 900 performs iterative decoding while exchanging log likelihood ratios, performs decoding such as turbo decoding, and performs decoding at a coding rate of 1/3.

(Embodiment 8)
In the second embodiment, encoding that creates an LDPC-CC having a time-varying period g (g is a natural number) that can correspond to a plurality of encoding rates (r-1) / r (r is an integer of 2 to q). The vessel was explained. In the present embodiment, another LDPC-CC having a time-varying period g (g is a natural number) that can correspond to a plurality of coding rates (r-1) / r (r is an integer not less than 2 and not more than q) is generated. The structural example of an encoder is shown.

  FIG. 39 is a configuration example of the encoder according to the present embodiment. In the encoder of FIG. 39, the same reference numerals as those in FIG.

  The encoder 800 in FIG. 37 is an encoder in which the parity calculation unit 830 obtains a parity of coding rates 1/2, 2/3, 3/4, and 4/5. The parity calculation unit 840 includes a code Whereas the encoder 800A shown in FIG. 39 has both a parity operation unit 830A and a parity operation unit 840A, for example, when the encoding rate is 2/3, the encoder 800A in FIG. The LDPC-CC encoding with variable period 3 is performed, and the parity calculation unit 830A and the parity calculation unit 840A are codes defined by different parity check polynomials.

  The control unit 820A performs control so that information is not input to the parity calculation unit 840A when the coding rate setting unit 810 designates the coding rate 2/3. Further, the control unit 820A controls the same information as the information input to the parity calculation unit 830A to be input to the parity calculation unit 840A when the coding rate 1/2 is set.

  The parity calculation unit 830A is an encoder that obtains a parity with an encoding rate of 2/3 defined by, for example, Expression (45-1), Expression (45-2), and Expression (45-3). When the coding rate setting unit 810 designates coding rates 1/2 and 2/3, the parity calculation unit 830A outputs the parity P.

  The parity calculation unit 840A is an encoder that obtains a parity with an encoding rate of 2/3 defined by a parity check polynomial different from that of the parity calculation unit 830A. Only when the coding rate setting unit 810 specifies the coding rate 1/2, the parity calculation unit 840A outputs the parity Pa.

  Thus, when coding rate 1/2 is designated, encoder 800A outputs parity P and parity Pa for 2 bits of information, so that encoder 800A reduces coding rate 1/2. Can be realized.

  Of course, in FIG. 39, the coding rate of the parity calculation unit 830A and the parity calculation unit 840A is not limited to 2/3, and may be a coding rate of 3/4, 4/5,. It suffices that both the parity calculation unit 830A and the parity calculation unit 840A have the same coding rate.

  The embodiment of the present invention has been described above. The invention related to LDPC-CC described in the first to fourth embodiments and the invention related to the relationship between the information size and the termination size described in the fifth and subsequent embodiments are independently established. .

  Further, the present invention is not limited to all the embodiments described above, and can be implemented with various modifications. For example, in the above-described embodiment, the description has been mainly given of the case where it is realized by an encoder and a decoder. However, the present invention is not limited to this, and can also be applied when realized by a power line communication device. is there.

  It is also possible to perform this encoding method and decoding method as software. For example, a program for executing the encoding method and the communication method may be stored in advance in a ROM (Read Only Memory), and the program may be operated by a CPU (Central Processor Unit).

  Further, a program for executing the encoding method and the decoding method is stored in a computer-readable storage medium, the program stored in the storage medium is recorded in a RAM (Random Access Memory) of the computer, and the computer is stored in the storage medium. You may make it operate | move according to a program.

  Needless to say, the present invention is useful not only in wireless communication but also in power line communication (PLC), visible light communication, and optical communication.

  The receiving apparatus and the receiving method according to the present invention can avoid the deterioration of the information transmission efficiency without deteriorating the error correction capability even when the termination is performed.

DESCRIPTION OF SYMBOLS 100 LDPC-CC encoder 110 Data operation part 120,230,632,830,830A, 840,840A Parity operation part 130,260 Weight control part 140 mod2 adder 111-1 to 111-M, 121-1 to 121 -M, 221-1 to 221-M, 231-1 to 231-M Shift registers 112-0 to 112-M, 122-0 to 122-M, 222-0 to 222-M, 232-0 to 232- M Weight Multiplier 200, 630, 630A, 800, 800A Encoder 210 Information Generation Unit 220-1 First Information Operation Unit 220-2 Second Information Operation Unit 220-3 Third Information Operation Unit 240 Addition Unit 250, 610 810 coding rate setting unit 300 720 900 decoding unit 310 log likelihood ratio setting unit 320 matrix processing operation unit 32 DESCRIPTION OF SYMBOLS 1 Memory | storage part 322 Row processing calculating part 323 Column processing calculating part 400,500,600,600A, 700,700A Communication apparatus 410 Coding rate determination part 420,640 Modulation part 510 Receiving part 520 Log likelihood ratio generation part 530,710 Control information generation unit 620 Transmission information generation and information length detection unit 631 Termination sequence length determination unit 633, 730 Coding rate adjustment unit 820, 820A, 910 Control unit 920, 930 BP decoding unit

Claims (6)

When configured information sequence of a plurality of bits, is added to the information sequence, coding using the known information that changes according to the coding rate for the low density parity check convolutional code (LDPC-CC) A receiving unit for receiving a signal including a parity bit generated by calculation and the information sequence;
Depending on the coding rate used for the coding operation of the LDPC-CC are included in the reception signal, the control information generating unit which determines the length of the known information,
A likelihood ratio generating unit that generates a likelihood corresponding to the known information according to a length of the known information, and generates a likelihood of the information sequence and a likelihood of the parity bit from the received signal;
A decoding unit that decodes the information sequence by performing a decoding operation using the likelihood of the information sequence, the likelihood of the parity bit, and the likelihood corresponding to the known information;
A receiving apparatus comprising: The known information is zero information.
The receiving device according to claim 1. The length of the known information has a plurality of types for each coding rate,
The control information generation unit
Furthermore, according to the sequence length of the information sequence, the length of the known information is determined from the plurality of types,
The receiving device according to claim 1 or 2. When configured information sequence of a plurality of bits, is added to the information sequence, coding using the known information that changes according to the coding rate for the low density parity check convolutional code (LDPC-CC) Receiving a signal including a parity bit generated by the operation and the information sequence;
Depending on the coding rate used for the coding operation of the LDPC-CC are included in the reception signal, to determine the length of the known information,
According to the length of the known information, a likelihood corresponding to the known information is generated, and the likelihood of the information sequence and the likelihood of the parity bit are generated from the received signal,
Using the likelihood of the information sequence, the likelihood of the parity bit, and the likelihood corresponding to the known information, a decoding operation is performed to decode the information sequence.
Reception method. The known information is zero information.
The receiving method according to claim 4. The length of the known information has a plurality of types for each coding rate,
The length of the known information is further determined from the plurality of types of the length of the known information according to a sequence length of the information sequence.
The receiving method according to claim 4 or 5.

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