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Quasi-Cyclic Low-Density Parity-Check Codes

  • Marco BaldiEmail author
Chapter
Part of the SpringerBriefs in Electrical and Computer Engineering book series (BRIEFSELECTRIC)

Abstract

In this chapter, we describe the main characteristics of a hybrid class of codes which are both quasi-cyclic (QC) and low-density parity-check (LDPC) codes. They join the powerful error correcting performance of LDPC codes with the structured nature of QC codes, which allows for very compact representations. This, together with the high number of equivalent codes, makes these codes well suited for cryptographic applications. This chapter addresses the design of these codes, as well as the estimation of the number of different codes having the same parameters.

Keywords

QC-LDPC codes QC-MDPC codes Difference families Equivalent codes 

References

  1. 1.
    Lin S, Costello DJ (2004) Error control coding, 2nd edn. Prentice-Hall Inc, Upper Saddle RiverGoogle Scholar
  2. 2.
    Townsend R, Weldon JE (1967) Self-orthogonal quasi-cyclic codes. IEEE Trans Inform Theory 13(2):183–195CrossRefzbMATHGoogle Scholar
  3. 3.
    Kou Y, Lin S, Fossorier M (2001) Low-density parity-check codes based on finite geometries: a rediscovery and new results. IEEE Trans Inform Theory 47(7):2711–2736CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Chen L, Xu J, Djurdjevic I, Lin S (2004) Near-shannon-limit quasi-cyclic low-density parity-check codes. IEEE Trans Commun 52(7):1038–1042CrossRefGoogle Scholar
  5. 5.
    CCSDS (2006) Low density parity check codes for use in near-earth and deep space applications. Tech Rep Orange Book, Issue 1, Consultative Committee for Space Data Systems (CCSDS), Washington, DC, USAGoogle Scholar
  6. 6.
    Li Z, Kumar B (2004) A class of good quasi-cyclic low-density parity check codes based on progressive edge growth graph. In: Proceedings of 38th Asilomar conference on signals, systems and computers, vol 2, Pacific Grove, USA, pp 1990–1994Google Scholar
  7. 7.
    Hu XY, Eleftheriou E, Arnold DM (2005) Regular and irregular progressive edge-growth tanner graphs. IEEE Trans Inform Theory 51:386–398CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Tanner R, Sridhara D, Fuja T (2001) A class of group-structured LDPC codes. In: Proceedings of ISTA 2001, Ambleside, EnglandGoogle Scholar
  9. 9.
    Fossorier MPC (2004) Quasi-cyclic low-density parity-check codes from circulant permutation matrices. IEEE Trans Inform Theory 50(8):1788–1793CrossRefMathSciNetGoogle Scholar
  10. 10.
    Thorpe J, Andrews K, Dolinar S (2004) Methodologies for designing LDPC codes using protographs and circulants. In: Proceedings of IEEE international symposium on information theory (ISIT), Chicago, USA, p 236Google Scholar
  11. 11.
    Kim S, No JS, Chung H, Shin DJ (2007) Quasi-cyclic low-density parity-check codes with girth larger than 12. IEEE Trans Inform Theory 53(8):2885–2891CrossRefMathSciNetGoogle Scholar
  12. 12.
    (2005) IEEE standard for local and metropolitan area networks. Part 16: air interface for fixed and mobile broadband wireless access systems. Amendment 2: physical and medium access control layers for combined fixed and mobile operation in licensed bands. 802.16e-2005Google Scholar
  13. 13.
    Hocevar D (2003) LDPC code construction with flexible hardware implementation. In: Proceedings of IEEE international conference on communications (ICC ’03), vol 4, Anchorage, USA, pp 2708–2712Google Scholar
  14. 14.
    Hocevar D (2003) Efficient encoding for a family of quasi-cyclic LDPC codes. In: Proceedings of IEEE global telecommunications conference (GLOBECOM ’03), vol 7, San Francisco, USA, pp 3996–4000Google Scholar
  15. 15.
    MacKay DJC, Davey M (1999) Evaluation of Gallager codes for short block length and high rate applications. In: Proceedings of IMA workshop codes, systems and graphical models. http://dx.doi.org/10.1007/978-1-4613-0165-3_6
  16. 16.
    Kamiya N (2007) High-rate quasi-cyclic low-density parity-check codes derived from finite affine planes. IEEE Trans Inform Theory 53(4):1444–1459CrossRefMathSciNetGoogle Scholar
  17. 17.
    Baldi M, Bambozzi F, Chiaraluce F (2011) On a family of circulant matrices for quasi-cyclic low-density generator matrix codes. IEEE Trans Inform Theory 57(9):6052–6067CrossRefMathSciNetGoogle Scholar
  18. 18.
    Johnson S, Weller S (2003) A family of irregular LDPC codes with low encoding complexity. IEEE Commun Lett 7(2):79–81Google Scholar
  19. 19.
    Vasic B, Milenkovic O (2004) Combinatorial constructions of low-density parity-check codes for iterative decoding. IEEE Trans Inform Theory 50(6):1156–1176CrossRefMathSciNetGoogle Scholar
  20. 20.
    Fujisawa M, Sakata S (2005) A class of quasi-cyclic regular LDPC codes from cyclic difference families with girth 8. In: Proceedings of international symposium on information theory (ISIT 2005), Adelaide, Australia, pp 2290–2294Google Scholar
  21. 21.
    Baldi M, Chiaraluce F (2005) New quasi cyclic low density parity check codes based on difference families. In: Proceedings of 8th international symposium on communication theory and applications, ISCTA 05, Ambleside, UK, pp 244–249Google Scholar
  22. 22.
    Xia T, Xia B (2005) Quasi-cyclic codes from extended difference families. In: Proceedings of IEEE wireless communications and networking conference, vol 2, New Orleans, USA, pp 1036–1040Google Scholar
  23. 23.
    CCSDS (2012) TM synchronization and channel coding—summary of concept and rationale. Green Book, Consultative Committee for Space Data Systems (CCSDS), CCSDS 130.1-G-2Google Scholar
  24. 24.
    Misoczki R, Tillich JP, Sendrier N, Barreto P (2013) MDPC-McEliece: New McEliece variants from moderate density parity-check codes. In: Proceedings of IEEE international symposium on information theory (ISIT 2013), Istanbul, Turkey, pp 2069–2073Google Scholar
  25. 25.
    Baldi M, Bianchi M, Chiaraluce F (2013) Optimization of the parity-check matrix density in QC-LDPC code-based McEliece cryptosystems. In: Proceedings of IEEE ICC (2013) workshop on information security over noisy and lossy communication systems. Budapest, HungaryGoogle Scholar

Copyright information

© The Author(s) 2014

Authors and Affiliations

  1. 1.DIIUniversità Politecnica delle MarcheAnconaItaly

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