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.
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References
Lin S, Costello DJ (2004) Error control coding, 2nd edn. Prentice-Hall Inc, Upper Saddle River
Townsend R, Weldon JE (1967) Self-orthogonal quasi-cyclic codes. IEEE Trans Inform Theory 13(2):183–195
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):2711–2736
Chen L, Xu J, Djurdjevic I, Lin S (2004) Near-shannon-limit quasi-cyclic low-density parity-check codes. IEEE Trans Commun 52(7):1038–1042
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, USA
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 1990–1994
Hu XY, Eleftheriou E, Arnold DM (2005) Regular and irregular progressive edge-growth tanner graphs. IEEE Trans Inform Theory 51:386–398
Tanner R, Sridhara D, Fuja T (2001) A class of group-structured LDPC codes. In: Proceedings of ISTA 2001, Ambleside, England
Fossorier MPC (2004) Quasi-cyclic low-density parity-check codes from circulant permutation matrices. IEEE Trans Inform Theory 50(8):1788–1793
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 236
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):2885–2891
(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-2005
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 2708–2712
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 3996–4000
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
Kamiya N (2007) High-rate quasi-cyclic low-density parity-check codes derived from finite affine planes. IEEE Trans Inform Theory 53(4):1444–1459
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):6052–6067
Johnson S, Weller S (2003) A family of irregular LDPC codes with low encoding complexity. IEEE Commun Lett 7(2):79–81
Vasic B, Milenkovic O (2004) Combinatorial constructions of low-density parity-check codes for iterative decoding. IEEE Trans Inform Theory 50(6):1156–1176
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 2290–2294
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 244–249
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 1036–1040
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-2
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 2069–2073
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, Hungary
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Baldi, M. (2014). Quasi-Cyclic Low-Density Parity-Check Codes. In: QC-LDPC Code-Based Cryptography. SpringerBriefs in Electrical and Computer Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-02556-8_4
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DOI: https://doi.org/10.1007/978-3-319-02556-8_4
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