Nothing Special   »   [go: up one dir, main page]

Skip to main content

2-Stripes Block-Circulant LDPC Codes for Single Bursts Correction

  • Conference paper
  • First Online:
Intelligent Interactive Multimedia Systems and Services 2016

Part of the book series: Smart Innovation, Systems and Technologies ((SIST,volume 55))

Abstract

In this paper the low-density parity-check (LDPC) codes are considered applied to correction of error bursts. Errors grouping and forming of so-called bursts are typical effect in real communication and data storage systems, however, this effect is typically ignored, and the coding task is reduced to correction of independent errors, which makes the practical characteristics of coding systems worse comparing to possibly reachable. Nevertheless, LDPC codes are able to protect from burst errors as well as independent ones. The main result of the paper is dedicated to evaluation of maximum correctable burst length of Gilbert codes, which are the 2-stripes special case of LDPC block-permutation codes, the construction which is often used in modern practical applications and research.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Proakis, J., Salehi, M.: Digital Communications. McGraw-Hill (2007)

    Google Scholar 

  2. Krouk, E.A., Ovchinnikov, A.A.: Metrics for distributed systems. In: 2014 XIV International Symposium on Problems of Redundancy in Information and Control Systems (REDUNDANCY), pp. 66–70, 1–5 June 2014

    Google Scholar 

  3. Krouk, E., Semenov, S., authors.: Krouk, E., Semenov, S. (eds.) Modulation and Coding Techniques in Wireless Communications. Wiley (2011)

    Google Scholar 

  4. MacWilliams, F., Sloane, N.: The Theory of Error-Correcting Codes. North-Holland Publishing Company (1977)

    Google Scholar 

  5. Lin, S., Ryan, W.: Channel Codes: Classical and Modern. Cambridge University Press (2009)

    Google Scholar 

  6. Gallager, R.G.: Low density parity check codes. IRE Trans. Inf. Theory (1962)

    Google Scholar 

  7. Gallager, R.G.: Low Density Parity Check Codes. MIT Press, Cambridge, MA (1963)

    MATH  Google Scholar 

  8. MacKay, D.: Good error correcting codes based on very sparse matrices. IEEE Trans. Inf. Theory 45 (1999)

    Google Scholar 

  9. MacKay, D., Neal, R.: Near shannon limit performance of low-density parity-check codes. IEEE Trans. Inf. Theory 47(2) (2001)

    Google Scholar 

  10. Richardson, T.J., Urbanke, R.L.: The capacity of low-density parity-check codes under message-passing decoding. IEEE Trans. Inf. Theory 47(2) (2001)

    Google Scholar 

  11. Zyablov, V., Pinsker, M.: Estimation of the error-correction complexity for Gallager low-density codes. Probl. Inf. Trans. XI(1), 18–28 (1975)

    MATH  Google Scholar 

  12. Forney, G.D., Richardson, T.J., Urbanke, R.L., Chung, S.-Y.: On the design of low-density parity-check codes within 0.0045 db of the Shannon Limit. IEEE Commun. Lett. 5(2) (2001)

    Google Scholar 

  13. Kozlov, A., Krouk, E., Ovchinnikov, A.: An approach to development of block-commutative codes with low density of parity check. Izvestiya vuzov. Priborostroenie. 8, 9–14 (2013). (In Russian)

    Google Scholar 

  14. Gilbert, E.N.: A problem in binary encoding. Proc. Symp. Appl. Math. 10, 291–297 (1960)

    Article  MathSciNet  MATH  Google Scholar 

  15. Arazi, B.: The optimal Burst error-correcting capability of the codes generated by \(f(x)=(x^p+1)(x^q+1)/(x+1)\). Inf. Contr. 39(3), 303–314 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  16. Bahl, L.R., Chien, R.T.: On Gilbert Burst-error-correcting codes. IEEE Trans. Inf. Theory 15(3) (1969)

    Google Scholar 

  17. Neumann, P.G.: A note on Gilbert Burst-correcting codes. IEEE Trans. Inf. Theory, IT-11:377 (1965)

    Google Scholar 

  18. Zhang, W., Wolf, J.: A class of Binary Burst error-correcting quasi-cyclic codes. IEEE Trans. Inf. Theory, IT-34:463–479 (1988)

    Google Scholar 

  19. Krouk, E., Ovchinnikov, A.: 3-Stripes Gilbert low density parity-check codes. US Patent 7,882,415

    Google Scholar 

  20. Krouk, E.A., Semenov, S.V.: Low-density parity-check Burst error-correcting codes. In: International Workshop Algebraic and Combinatorial Coding Theory, Leningrad, pp. 121–124 (1990)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Andrei Ovchinnikov .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Krouk, E., Ovchinnikov, A. (2016). 2-Stripes Block-Circulant LDPC Codes for Single Bursts Correction. In: Pietro, G., Gallo, L., Howlett, R., Jain, L. (eds) Intelligent Interactive Multimedia Systems and Services 2016. Smart Innovation, Systems and Technologies, vol 55. Springer, Cham. https://doi.org/10.1007/978-3-319-39345-2_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-39345-2_2

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-39344-5

  • Online ISBN: 978-3-319-39345-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics