CN104378122B - A kind of Compilation Method of variable-length Turbo code - Google Patents
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Abstract
The invention discloses a kind of Compilation Method of variable-length Turbo code, the interpretation method of coding method and variable-length Turbo code including variable-length Turbo code, using the rule of the information sequence length generally less than original information sequence length transmitted in Turbo code is shortened, ranked again by the carrying out of the information sequence bit on the basis of Turbo code mother's code to shortening, the low bit error rate position that the bit of the information of transmission is placed in bit error rate distribution curve, will not transmit the bit of information（The bit of zero setting）It is placed in the position of high bit error rate; make full use of the feature of the unequal loss protection that Turbo code has in itself; Given information in information sequence is made full use of in the case of hardly changing coding and decoding method; the length that both can arbitrarily change input message sequence is reached, the effect of information reliability can be ensured again.
Description
Technical field
The present invention relates to a kind of Compilation Method of Turbo code, more particularly to a kind of compiling side of variable-length Turbo code
Method.
Background technology
In data communication, for the reliability of enhancement information transmission, data are existed using the method for channel coding generally
The mistake produced in transmission is detected and corrected.Turbo code is a kind of error correcting code of the excellent performance for developing in the recent decade,
With extraordinary error correcting capability, systematic function can be substantially improved.The component code simple structure of Turbo code, it is easy to accomplish, and
Each component code can use parallel decoding, reach data rate higher, be very suitable for high-performance, the communication system of high-throughput
System, there is good application prospect.But traditional Turbo code belongs to block code, it is desirable to which message length is isometric.And having
Under a little communication environments, such as in network communications, message length is variable.In order to adapt to different message lengths, it is necessary to grind
Study carefully the channel coding problem of variable-length.
The patent of invention of Application No. 200510114754《Integrated source and channel variable-length symbol Turbo coding and decoding methods》
Disclose a kind of integrated source and channel variable-length symbol Turbo coding and decoding methods.The variable length that the method is exported to message sink coding
Codeword sequence is classified according to code length and probability, carries out unequal error protection, and code word packet sequence probability of occurrence long is small, level
It is not less important, encoded using the Turbo code of code check high；The short packet sequence probability of occurrence of code word is larger, and rank is heavier
Will, encoded using the Turbo code of low bit- rate.Although this method uses variable-length symbol Turbo encoding and decoding algorithms, pass through
Variable-length symbol is encoded and the judgement of elongated symbol substitution, it is possible to increase the performance of communications system transmission and the efficiency of joint decoding.
But in this approach, it assumes that " code word packet sequence probability of occurrence long is small, and rank is less important, and code word is short to divide first
Group sequence probability of occurrence is larger, and rank is more important " do not have generality.Secondly, it is variable that the method is exported to source encoder
Long code word sequence is classified according to code word size, and code word more long is classified as one group, and shorter code word is classified as one group, rather than right
Message sink coding its output code word directly encoded, directly influence the efficiency of coding.
The patent of invention of Application No. 201010289187.3《Shorten the coding and decoding method of Turbo product codes》Disclose one
Plant the coding and decoding method of the Turbo code of variable-length.The patent is related to a kind of volume of the shortening Turbo product codes based on BCH code
Interpretation method.The specific steps of coding method include：Treating coded information sequences carries out row or column coding；Row or column is encoded and is produced
Raw row or column component code code word carries out parallel encoding；Judge whether coding completes.The specific steps of interpretation method include：Generation
The hard decision sequence of soft input message sequence；Least reliable bits are selected in soft input message sequence；According to hard decision sequence and
Least reliable bits generate cycle tests；To cycle tests decoding generation candidate codewords；Calculate candidate codewords and soft input information sequence
The measurement of row；Reduce candidate codewords number；Measurement according to candidate codewords determines judgement code word；Calculate each code in judgement code word
The external information of unit.Although the coding method in the patent can improve data throughout, coding delay is reduced；Interpretation method can
Substantial amounts of logical resource and storage resource are saved, especially in the case where component code code length is larger, can be good at balance decoding
Complexity and data throughout.But this method is to be compiled code as the component code of Turbo code based on BCH block codes,
Its bit error rate shows bad under middle signal to noise ratio.In addition, the method is based on the BCH product codes for shortening, to different Chief Information Officers
The adaptability of degree is poor.
The content of the invention
It is an object of the invention to provide a kind of compiling side of the variable-length Turbo code set up on the basis of a female code
Method, the ranking again of information sequence bit that can be in the case where hardly coding and decoding method is changed to shortening, and in decoding
In make full use of Given information in information sequence, reach the length that both can arbitrarily change input message sequence, and letter can be ensured
Cease the effect of reliability.
The present invention uses following technical proposals：
A kind of Compilation Method of variable-length Turbo code, including variable-length Turbo code coding method and variable-length
The interpretation method of Turbo code；
The coding method of variable-length Turbo code is comprised the following steps：
A：Determine Turbo code mother's code, the information sequence length of Turbo code mother's code is k, and code check is R, generator polynomial
Matrix is g=(1, g (D)/h (D)), and gives interleaver type and censoring matrix；
B：Monte Carlo simulation is carried out under conditions of given signal to noise ratio snr to Turbo code mother's code, bit error rate point is obtained
Cloth Pb=(p1, p2 ..., pk), P in formulabJ ()=pj, j=1,2 ..., k, k are information sequence length；PbJ () is female Turbo code
J-th error rate of information bit position in code；
C：To bit error rate distribution curve PbSize according to the bit error rate of each information bit position is entered from small to large
Row rearrangement, obtains sequencing table ∏=(π 1, π 2, the π 3 ..., π k) of change in location, ∏ (j)=π j, j=1,2 ... in formula,
k；
D：If the information sequence length that Turbo code mother's code is actually entered after shortening is k`, the information sequence of input is Info
=(a1, a2 ..., ak`), Info (j)=aj, j=1,2 ..., k` in formula；In tail of sequence addition k-k` zero, sequence is obtained
Info`=(0 ... 0) for a1, a2, a3 ..., ak`, i.e., preceding k` for shorten after information sequence, rear k-k` zero padding, k`≤k,
aj=0 or 1；
E：Each information bit in information sequence Info` after zero padding is resequenced according to sequencing table ∏, if row
Information sequence after sequence is expressed as Info``, then Info`` (∏ (j))=Info` (j), j=1,2 ..., k, obtain new information
Sequence Info``=(b1, b2 ..., bk), j=1,2 ..., k；
F：The information sequence Info`` feeding Turbo code encoders that will be obtained after sequence are encoded, and obtain two-way verification
Sequence P1 and P2；
G：By information sequence Info and two-way verification sequence P1 and P2 composition codeword sequence Codeword；
H：BPSK modulation is carried out to codeword sequence Codeword, modulated signal sequences Modu is generated and is sent into channel transmission；
Modu (j)=2 × Codeword (j) -1；
The interpretation method of variable-length Turbo code is comprised the following steps：
I：Receiving terminal is received it is corresponding with modulated signal sequences Modu be interfered after receiving sequence Re in
Each road information is separated, respectively obtain with input message sequence Info, two-way deliver for a check the corresponding sequence S1 of sequence P1 and P2,
Pr1 and Pr2, wherein S1=(s1, s2 ..., sk`)；
J：The sequence S1 that will be received is extended, i.e., k-k` negative G, G are added after sequence S1 less than or equal to -200, is obtained
To sequence spreading S1`, S1`=(s1, s2 ..., sk`, G ..., G)；
K：Sequence spreading S1` is resequenced according to sequencing table ∏, sequence S1``, the S1`` (∏ after being sorted
(j))=S1` (j), j=1,2 ..., k；
L：Sequence S1``, Pr1 and Pr2 feeding Turbo code decoders are iterated decoding, decoding terminates rear output information
Valuation the sequence S2, S2=(t1, t2 ..., tk) of sequence；
M：Position inverse transformation is carried out according to sequencing table ∏ to valuation sequence S2, that is, recovers original order, be restored order
Sequence S3 afterwards, position contravariant is changed to：S3 (j)=S2 (∏ (j)), j=1,2 ..., k；
N：Preceding k` of S3 is taken, last decoding result is obtained.
In described step B, signal to noise ratio snr should make average error bit rate be more than or equal to 10-4And less than or equal to 10-3；Emulation
Bit is no less than k × 105, k is information sequence length.
In described J steps, G=-500.
The present invention is using the information sequence length generally less than original information sequence length transmitted in Turbo code is shortened
Rule, ranked again by the carrying out of information sequence bit to shortening on the basis of Turbo code mother's code, by the information of transmission
The low bit error rate position that bit is placed in bit error rate distribution curve, the bit (bit of zero setting) that will not transmit information is placed in
The position of high bit error rate, makes full use of the feature of the unequal loss protection that Turbo code has in itself, is hardly changing coding and decoding
The Given information in information sequence is made full use of in the case of method, the length that both can arbitrarily change input message sequence is reached,
The effect of information reliability can be ensured again.
Brief description of the drawings
Fig. 1 is bit error rate scatter chart before and after rearrangement；
Fig. 2 is the average error bit rate curve under difference information sequence length before information sequence is reset；
Fig. 3 is the average error bit rate curve under different information sequence length after information sequence is reset；
Fig. 4 is the flow chart of the coding method of variable-length Turbo code in the present invention；
Fig. 5 is the flow chart of the interpretation method of variable-length Turbo code in the present invention；
Fig. 6 is bit error rate distribution curve of the Turbo code mother's code before and after rearranging in embodiment 1；
Fig. 7 is Turbo code mother's code change table in bit position before and after rearrangement in embodiment 1.
Specific embodiment
In Turbo code, a bit error rate distribution P for codeb=(p1, p2 ..., pk) is uneven, in formula, Pb(j)
=pj, j=1,2 ..., k, k are information sequence length, PbJ () is j-th error probability of information bit.Some information bits
Error probability it is higher, and the error probability of some information bits is lower.As shown in figure 1, Fig. 1 gives the length that interweaves
Spend for 64 Turbo code signal to noise ratio be 4dB under bit error rate distribution curve.The generator polynomial matrix of Turbo code is g=
(1,D4+1/D4+D3+D2+ D+1), g=(1, g (D)/h (D)) is general expression, is translated into embodies in this example
Formula g=(1, D4+1/D4+D3+D2+ D+1), using the Block Interleaver of 8 × 8, censoring matrix is (10；, therefore code check 01)
It is 1/2.Curve A in Fig. 1 is the bit error rate distribution curve before sequence, i.e. raw bit error rate distribution curve.Can be with by Fig. 1
Find out, it is low that the error rate of each information bit has height to have, staggeredly irregular.Curve B is will be each in former bit error rate distribution curve
The bit error rate of individual information bit rearranges what is obtained according to order from low to high.In Turbo code is shortened, transmitted
Information sequence length is generally less than original information sequence length, and the bit of the information of transmission is placed in bit error rate by us as far as possible
Low bit error rate position in distribution curve, the bit (bit of zero setting) that will not transmit information is placed in the position of high bit error rate
Put, can so make full use of the feature of the unequal loss protection that Turbo code has in itself so that information bit is preferably protected
Shield.
When the information of transmission, the bit being zeroed out in information sequence need not be transmitted.It is assumed that being modulated using BPSK, modulation
Rule be 0 → -1,1 →+1, in receiving terminal, although the bit being zeroed out is not transmitted, but they position and value be known
's.Therefore, before receiving sequence enters row decoding, the value of the bit that will be zeroed out is replaced with a sufficiently large negative, repeatedly
These known information can be just made full use of during generation decoding, decoding efficiency is improved.
Fig. 2 and Fig. 3 sets forth under different information sequence length, the average mistake before and after resetting under different signal to noise ratios
Bit rate curve.Fig. 2 is the average error bit rate curve under difference information sequence length before information sequence is reset, and Fig. 3 is information
Average error bit rate curve after sequence reorganization under different information sequence length.Information sequence length takes 64 (equivalent to not having respectively
Have shortening), 16,32,52.From figure 3, it can be seen that after information sequence is reset, the mean bit error under different message lengths
Rate is obtained for obvious improvement.During such as signal to noise ratio 6dB, shortening the average error bit rate after Turbo code has a quantity
The improvement of level or so.
Using above-mentioned principle, as shown in Figure 4 and Figure 5, the Compilation Method of variable-length Turbo code of the present invention, bag
Include the coding method of variable-length Turbo code and the interpretation method of variable-length Turbo code；
Wherein, the coding method of variable-length Turbo code is comprised the following steps：
A：Determine Turbo code mother's code, the information sequence length of Turbo code mother's code is k, and code check is R, generator polynomial
Matrix is g=(1, g (D)/h (D)), and gives interleaver type and censoring matrix；
B：Monte Carlo simulation is carried out under conditions of given signal to noise ratio snr to Turbo code mother's code, bit error rate point is obtained
Cloth Pb=(p1, p2 ..., pk), P in formulabJ ()=pj, j=1,2 ..., k, k are information sequence length, PbJ () is female Turbo code
J-th error rate of information bit position in code；
When the selection of signal to noise ratio snr is carried out, average error bit rate is set to be more than or equal to 10-4And less than or equal to 10-3.
To obtain accurate bit error rate distribution, emulation bit should be more as far as possible, typically no less than k × 105, k is that information sequence is long
Degree.
When information sequence length is more long, such as k>105, bit error rate distribution PbIn, it is possible that the mistake of some code elements
Probability is zero situation, if zero number is less, such as, no more than 1 the percent of code word size, is not had for result bright
Aobvious influence.If zero number is excessive, can be by increasing the bit number for emulating, so as to improve simulation accuracy.
C：P is distributed to bit error ratebSize according to the bit error rate of each information bit position carries out weight from small to large
New sort, obtains sequencing table ∏=(π 1, π 2, the π 3 ..., π k) of change in location, ∏ (j) in formula=π j, j=1,2 ..., k.Row
The implication of sequence table ∏ is have minimum bit error rate in the bit of home position (before converting) π 1, is put in the first place after conversion；
Bit before conversion in home position π 2 has time bit error rate of minimum, and the 2nd position is placed on after conversion；..., conversion before
There is the small bit error rate of jth in the bit of home position π j, jth position is placed on after conversion；By that analogy.
D：If the information sequence length that Turbo code mother's code is actually entered after shortening is k`, the information sequence of input is Info
=(a1, a2 ..., ak`), Info (j)=aj, j=1,2 ..., k` in formula.In tail of sequence addition k-k` zero, sequence is obtained
Info`=(0 ... 0) for a1, a2, a3 ..., ak`, i.e., preceding k` for shorten after information sequence, rear k-k` zero padding, k`≤k,
aj=0 or 1；
E：Each information bit in information sequence Info` after zero padding is resequenced according to sequencing table ∏, if row
Information sequence after sequence is expressed as Info``, then Info`` (∏ (j))=Info` (j), j=1,2 ..., k, obtain new information
Sequence Info``=(b1, b2 ..., bk), j=1,2 ..., k；
F：The information sequence Info`` feeding Turbo code encoders that will be obtained after sequence are encoded, and obtain two-way verification
Sequence P1 and P2；
G：By information sequence Info and two-way verification sequence P1 and P2 composition codeword sequence Codeword；
H：BPSK modulation is carried out to codeword sequence Codeword, modulated signal sequences Modu is generated and is sent into channel transmission；
Modu (j)=2 × Codeword (j) -1；
The interpretation method of variable-length Turbo code is comprised the following steps：
I：Receiving terminal is received it is corresponding with modulated signal sequences Modu be interfered after receiving sequence Re in
Each road information is separated, and is respectively obtained and is delivered for a check the corresponding sequence of sequence P1 and P2 with the information sequence Info, two-way that are input into
S1, Pr1 and Pr2, wherein S1=(s1, s2 ..., sk`)；
J：The sequence S1 that will be received is extended, i.e., k-k` negative G, G are added after sequence S1 less than or equal to -200, is obtained
To sequence spreading S1`, S1`=(s1, s2 ..., sk`, G ..., G)；
K：Sequence spreading S1` is resequenced according to sequencing table ∏, sequence S1``, the S1`` (∏ after being sorted
(j))=S1` (j), j=1,2 ..., k；
L：Sequence S1``, Pr1 and Pr2 feeding Turbo code decoders are iterated decoding, decoding terminates rear output information
Valuation the sequence S2, S2=(t1, t2 ..., tk) of sequence；
M：Position inverse transformation is carried out according to sequencing table ∏ to valuation sequence S2, that is, recovers original order, be restored order
Sequence S3 afterwards, position contravariant is changed to：S3 (j)=S2 (∏ (j)), j=1,2 ..., k；
N：Preceding k` of S3 is taken, last decoding result is obtained.
The Compilation Method of variable-length Turbo code of the present invention is further explained below in conjunction with specific embodiment
State：
When the coding of variable-length Turbo code is carried out, performed successively according to following steps：
A：Turbo code mother's code is determined, if the generator polynomial matrix of Turbo code mother's code is g=(1, D2+1/D2+D+
1), g=(1, g (D)/h (D)) is general expression, and expression g=(1, D is translated into this example2+1/D2+D+
1), without censoring, code check is 1/3, and using a random interleaver, the information sequence length of Turbo code mother's code is 22, and end up sequence
Length is 2, and two-way encoder ends up；
B：Monte Carlo simulation is carried out under conditions of signal to noise ratio is 4dB to this Turbo code mother's code, bit error rate point is obtained
Cloth Pb, PbJ () is j-th error rate of information bit position in Turbo code mother's code, mistake ratio of the Turbo code mother's code before rearranging
Special rate distribution curve PbAs shown in the curve A in Fig. 6；
C：P is distributed to bit error ratebSize according to every bit error rate is resequenced from small to large, obtains position
The sequencing table ∏ of change, as shown in Figure 7；In the present embodiment, sequencing table ∏=(2 41536 14 19 22 7 15 9 10
21 8 20 16 18 17 13 11 12), bit error rate distribution curve P of the Turbo code mother's code after rearrangingbAs in Fig. 6
Curve B shown in；
D：If the information sequence length k`=8 that Turbo code is actually entered by after shortening, the information sequence of input is Info=
(a1, a2, a3, a4, a5, a6, a7, a8), by afterbody add 14 zero by the information sequence of input be expressed as Info`=(a1,
A2, a3, a4, a5, a6, a7, a8,0,0,0,0,0,0,0,0,0,0,0,0,0,0), i.e., preceding 8 is the information sequence after shortening,
14 (i.e. 22-8) position zero padding, a afterwardsj=0 or 1；
E：Each information bit in information sequence Info` is resequenced according to sequencing table according to sequencing table ∏, i.e.,
Info`` (∏ (j))=Info` (j), j=1,2 ..., k, after being sorted information sequence Info``=(a3, a1, a5, a2,
a4,a6,0,0,0,0,0,0,0,a7,0,0,0,0,a8,0,0,0)；
F：The information sequence Info`` feeding Turbo code encoders that will be obtained after sequence are encoded, and obtain two-way verification
Sequence P1 and P2；
G：By information sequence Info and two-way verification sequence P1 and P2 composition codeword sequence Codeword；
H：BPSK modulation is carried out to codeword sequence Codeword, modulated signal sequences Modu is generated and is sent into transmission,
Modu (j)=2 × Codeword (j) -1；
When the decoding of variable-length Turbo code is carried out, performed successively according to following steps：
I：Receiving terminal is received it is corresponding with modulated signal sequences Modu be interfered after receiving sequence Re in
Each road information is separated, and is respectively obtained and is delivered for a check the corresponding sequence S1 of sequence P1 and P2 with input message sequence Info, two-way,
Pr1 and Pr2, wherein S1=(s1, s2 ..., sk`)；
J：The sequence S1 that will be received is extended, i.e., k-k` negative G is added after sequence S1, herein, G values-
500, the sequence that is expanded S1`, S1`=(s1, s2 ..., sk`, -500 ..., -500)；
K：Sequence spreading S1` is resequenced according to sequencing table ∏, sequence S1``, the S1`` (∏ after being sorted
(j))=S1` (j)；S1``=(a3, a1, a5, a2, a4, a6, -500, -500, -500, -500, -500, -500, -500, a7, -
500,-500,-500,-500,a8,-500,-500,-500)
L：Sequence S1``, Pr1 and Pr2 feeding Turbo code decoders are iterated decoding, decoding terminates rear output information
Valuation the sequence S2, S2=(t1, t2 ..., tk) of sequence；
M：Position inverse transformation is carried out according to sequencing table ∏ to valuation sequence S2, the sequence S3=in the home position that is restored
(t2,t4,t1,t5,t3,t6,t14,t19,t22,t7,t15,t9,t10,t21,t8,t20,t16,t18,t17,t13,t11,
T12), i.e. S3 (j)=S2 (∏ (j))；
N：Take preceding k`=8 of S3, that is, obtain last decoding result, decoding result for (t2, t4, t1, t5, t3, t6,
t14,t19)。
Claims (3)
1. a kind of Compilation Method of variable-length Turbo code, it is characterised in that：Coding method including variable-length Turbo code
With the interpretation method of variable-length Turbo code；
The coding method of variable-length Turbo code is comprised the following steps：
A：Determine Turbo code mother's code, the information sequence length of Turbo code mother's code is k, and code check is R, generator polynomial matrix
It is g=(1, g (D)/h (D)), and given interleaver type and censoring matrix；
B：Monte Carlo simulation is carried out under conditions of given signal to noise ratio snr to Turbo code mother's code, bit error rate distribution P is obtainedb
=(p1, p2 ..., pk), uses PbJ () represents PbIn j-th element, i.e. PbJ ()=pj, j=1,2 ..., k, k are information sequence
Length；PbJ () is j-th error rate of information bit position in Turbo code mother's code；
C：To bit error rate distribution curve PbSize according to the bit error rate of each information bit position is carried out again from small to large
Sequence, obtains sequencing table ∏=(π 1, π 2, the π 3 ..., π k) of change in location, ∏ (j) in formula=π j, j=1,2 ..., k；
D：If the information sequence length that Turbo code mother's code is actually entered after shortening is k`, the information sequence of input is Info=
(a1, a2 ..., ak`), with j-th element in Info (j), i.e. Info (j)=aj, j=1,2 ..., k`；In tail of sequence addition
K-k` zero, obtain sequence Info`=(0 ... 0) for a1, a2, a3 ..., ak`, i.e., preceding k` is the information sequence after shortening, after
K-k` zero padding, k`≤k, aj=0 or 1；
E：Each information bit in information sequence Info` after zero padding is resequenced according to sequencing table ∏, if after sequence
Information sequence be expressed as Info``, then Info`` (∏ (j))=Info` (j), j=1,2 ..., k, obtain new information sequence
Info``=(b1, b2 ..., bk), j=1,2 ..., k；
F：The information sequence Info`` feeding Turbo code encoders that will be obtained after sequence are encoded, and obtain two-way verification sequence
P1 and P2；
G：By information sequence Info and two-way verification sequence P1 and P2 composition codeword sequence Codeword；
H：BPSK modulation is carried out to codeword sequence Codeword, modulated signal sequences Modu is generated and is sent into channel transmission；Modu
(j)=2 × Codeword (j) -1；
The interpretation method of variable-length Turbo code is comprised the following steps：
I：Receiving terminal is received it is corresponding with modulated signal sequences Modu be interfered after receiving sequence Re Zhong Ge roads
Information is separated, and is respectively obtained and is delivered for a check corresponding sequence S1, Pr1 of sequence P1 and P2 with input message sequence Info, two-way
And Pr2, wherein S1=(s1, s2 ..., sk`)；
J：The sequence S1 that will be received is extended, i.e., k-k` negative G, G are added after sequence S1 less than or equal to -200, is expanded
Exhibition sequence S1`, S1`=(s1, s2 ..., sk`, G ..., G)；
K：Sequence spreading S1` is resequenced according to sequencing table ∏, sequence S1``, S1`` (∏ (j)) after being sorted
=S1` (j), j=1,2 ..., k；
L：Sequence S1``, Pr1 and Pr2 feeding Turbo code decoders are iterated decoding, decoding terminates rear output information sequence
Valuation sequence S2, S2=(t1, t2 ..., tk)；
M：Position inverse transformation is carried out according to sequencing table ∏ to valuation sequence S2, that is, recovers original order, be restored after order
Sequence S3, position contravariant is changed to：S3 (j)=S2 (∏ (j)), j=1,2 ..., k；
N：Preceding k` of S3 is taken, last decoding result is obtained.
2. the Compilation Method of variable-length Turbo code according to claim 1, it is characterised in that：In described step B,
Signal to noise ratio snr should make average error bit rate be more than or equal to 10-4And less than or equal to 10-3；Emulation bit is no less than k × 105, k is letter
Breath sequence length.
3. the Compilation Method of variable-length Turbo code according to claim 2, it is characterised in that：In described J steps, G
=-500.
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| CN106452678B (en) * | 2016-10-21 | 2017-07-21 | 郑州大学西亚斯国际学院 | A kind of Turbo code puncturing method being distributed based on bit error rate |
| US10897295B2 (en) | 2017-04-13 | 2021-01-19 | Futurewei Technologies, Inc. | System and method for beam indexing reference signal design for initial access |
| CN109120377B (en) * | 2018-07-19 | 2020-11-27 | 华北水利水电大学 | Novel information hiding method in data transmission and storage medium |
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