A low complexity extrinsic message based decoding algorithm for non-binary LDPC codes

In this paper, we propose a low complexity extrinsic message based decoding algorithm for non-binary LDPC codes. This algorithm only requires computations over finite field and integer operations. The novelty of this decoding algorithm lies in that we compute extrinsic message and iteratively update the messages in every iteration. The proposed algorithm provides effective trade-off between computational complexity and performance. Furthermore, complexity issues and decoding performance will be well analyzed in this paper. Simulation results show that we can achieve a better performance than ISRB algorithm with a slight increase in computational complexity.

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

[2]  Qin Huang,et al.  Two Low-Complexity Reliability-Based Message-Passing Algorithms for Decoding Non-Binary LDPC Codes , 2010, IEEE Transactions on Communications.

[3]  Mark F. Flanagan,et al.  Serial Symbol-Reliability Based Algorithm for Decoding Non-Binary LDPC Codes , 2012, IEEE Communications Letters.

[4]  Dimitrios Makrakis,et al.  Optimal decoding of coded PSK and QAM signals in correlated fast fading channels and AWGN: a combined envelope, multiple differential and coherent detection approach , 1994, IEEE Trans. Commun..

[5]  Xiaohu You,et al.  New insights into weighted bit-flipping decoding , 2009, IEEE Transactions on Communications.

[6]  Baoming Bai,et al.  Nonbinary LDPC codes constructed based on a cyclic MDS code and a low-complexity nonbinary message-passing decoding algorithm , 2010, IEEE Communications Letters.

[7]  Yang Yu,et al.  Informed dynamic scheduling for majority-logic decoding of non-binary LDPC codes , 2013, 2013 IEEE Global Communications Conference (GLOBECOM).

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

[9]  David Declercq,et al.  Decoding Algorithms for Nonbinary LDPC Codes Over GF$(q)$ , 2007, IEEE Transactions on Communications.

[10]  Satoshi Goto,et al.  An efficient majority-logic based message-passing algorithm for non-binary LDPC decoding , 2012, 2012 IEEE Asia Pacific Conference on Circuits and Systems.

[11]  Shu Lin,et al.  Transactions Papers - Constructions of Nonbinary Quasi-Cyclic LDPC Codes: A Finite Field Approach , 2008, IEEE Transactions on Communications.

[12]  Yang Yu,et al.  Design of Convergence-Optimized Non-Binary LDPC Codes over Binary Erasure Channel , 2012, IEEE Wireless Communications Letters.

[13]  Valentin Savin,et al.  Min-Max decoding for non binary LDPC codes , 2008, 2008 IEEE International Symposium on Information Theory.

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