Concatenated finite geometry and finite field LDPC codes

This paper presents two types of concatenated finite-geometry and finite-field LDPC codes which have the distinct features of both finite geometry and finite field LDPC codes, such as large minimum distances, no small trapping sets, fast decoding convergence, capable of correcting both random errors and bursts of erasures, flexibility in code construction, cyclic and quasi-cyclic structures. It is shown that these concatenated codes are globally coupled LDPC codes and they perform well over the AWGN and binary erasure channels with a two-phase iterative decoding scheme.

[1]  D.J.C. MacKay,et al.  Good error-correcting codes based on very sparse matrices , 1997, Proceedings of IEEE International Symposium on Information Theory.

[2]  William E. Ryan,et al.  LDPC Code Designs, Constructions, and Unification , 2017 .

[3]  Thomas J. Richardson,et al.  Error Floors of LDPC Codes , 2003 .

[4]  Shu Lin,et al.  Error control coding : fundamentals and applications , 1983 .

[5]  Robert G. Gallager,et al.  Low-density parity-check codes , 1962, IRE Trans. Inf. Theory.

[6]  Khaled A. S. Abdel-Ghaffar,et al.  A Revolving Iterative Algorithm for Decoding Algebraic Cyclic and Quasi-Cyclic LDPC Codes , 2013, IEEE Transactions on Communications.

[7]  David J. C. MacKay,et al.  Weaknesses of Margulis and Ramanujan-Margulis low-density parity-check cCodes , 2003, MFCSIT.

[8]  Khaled A. S. Abdel-Ghaffar,et al.  Algebraic Quasi-Cyclic LDPC Codes: Construction, Low Error-Floor, Large Girth and a Reduced-Complexity Decoding Scheme , 2014, IEEE Transactions on Communications.

[9]  Qiuju Diao,et al.  LDPC Codes on Partial Geometries: Construction, Trapping Set Structure, and Puncturing , 2013, IEEE Transactions on Information Theory.

[10]  Qiuju Diao,et al.  A matrix-theoretic approach for analyzing quasi-cyclic low-density parity-check codes , 2012, IEEE Transactions on Information Theory.

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

[12]  Shu Lin,et al.  Channel Codes: Classical and Modern , 2009 .

[13]  Jinghu Chen,et al.  Near optimum universal belief propagation based decoding of low-density parity check codes , 2002, IEEE Trans. Commun..

[14]  Qiuju Diao,et al.  Cyclic and Quasi-Cyclic LDPC Codes on Constrained Parity-Check Matrices and Their Trapping Sets , 2012, IEEE Transactions on Information Theory.