Quasi-Cyclic Low-Density Parity-Check Codes

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.

[1]  Norifumi Kamiya,et al.  High-Rate Quasi-Cyclic Low-Density Parity-Check Codes Derived From Finite Affine Planes , 2005, IEEE Transactions on Information Theory.

[2]  Dale E. Hocevar.  Efficient encoding for a family of quasi-cyclic LDPC codes , 2003, GLOBECOM '03. IEEE Global Telecommunications Conference (IEEE Cat. No.03CH37489).

[3]  Marco Baldi,et al.  On a Family of Circulant Matrices for Quasi-Cyclic Low-Density Generator Matrix Codes , 2011, IEEE Transactions on Information Theory.

[4]  Dale E. Hocevar.  LDPC code construction with flexible hardware implementation , 2003, IEEE International Conference on Communications, 2003. ICC '03..

[5]  Marco Baldi,et al.  Optimization of the parity-check matrix density in QC-LDPC code-based McEliece cryptosystems , 2013, 2013 IEEE International Conference on Communications Workshops (ICC).

[6]  Samuel Dolinar,et al.  Methodologies for designing LDPC codes using protographs and circulants , 2004, International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings..

[7]  Shojiro Sakata,et al.  A class of quasi-cyclic regular LDPC codes from cyclic difference families with girth 8 , 2005, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005..

[8]  Marc P. C. Fossorier,et al.  Quasi-Cyclic Low-Density Parity-Check Codes From Circulant Permutation Matrices , 2004, IEEE Trans. Inf. Theory.

[9]  D. Mackay,et al.  Evaluation of Gallager Codes for Short Block Length and High Rate Applications , 2001 .

[10]  Shu Lin,et al.  Near-Shannon-limit quasi-cyclic low-density parity-check codes , 2004, IEEE Trans. Commun..

[11]  Sarah J. Johnson,et al.  A family of irregular LDPC codes with low encoding complexity , 2003, IEEE Communications Letters.

[12]  R. M. Tanner,et al.  A Class of Group-Structured LDPC Codes , 2001 .

[13]  R. Townsend,et al.  Self-orthogonal quasi-cyclic codes , 1967, IEEE Trans. Inf. Theory.

[14]  Evangelos Eleftheriou,et al.  Regular and irregular progressive edge-growth tanner graphs , 2005, IEEE Transactions on Information Theory.

[15]  Tao Xia,et al.  Quasi-cyclic codes from extended difference families , 2005, IEEE Wireless Communications and Networking Conference, 2005.

[16]  Sunghwan Kim,et al.  Quasi-Cyclic Low-Density Parity-Check Codes With Girth Larger Than $12$ , 2007, IEEE Transactions on Information Theory.

[17]  Ieee Microwave Theory,et al.  Part 16: Air Interface for Fixed and Mobile Broadband Wireless Access Systems — Amendment for Physical and Medium Access Control Layers for Combined Fixed and Mobile Operation in Licensed Bands , 2003 .

[18]  Shu Lin,et al.  Low-density parity-check codes based on finite geometries: A rediscovery and new results , 2001, IEEE Trans. Inf. Theory.

[19]  Paulo S. L. M. Barreto,et al.  MDPC-McEliece: New McEliece variants from Moderate Density Parity-Check codes , 2013, 2013 IEEE International Symposium on Information Theory.

[20]  Bane V. Vasic,et al.  Combinatorial constructions of low-density parity-check codes for iterative decoding , 2002, IEEE Transactions on Information Theory.

[21]  Zongwang Li,et al.  A class of good quasi-cyclic low-density parity check codes based on progressive edge growth graph , 2004, Conference Record of the Thirty-Eighth Asilomar Conference on Signals, Systems and Computers, 2004..