Bit-Reliability Based Low-Complexity Decoding Algorithms for Non-Binary LDPC Codes

This paper presents bit-reliability based majority-logic decoding (MLgD) algorithms for non-binary LDPC codes. The proposed algorithms pass only one Galois field element and its reliability along each edge of the Tanner graph of a non-binary LDPC code. Since their reliability updates are in terms of bits rather than symbols, they are more efficient than traditional MLgD based decoding algorithms. By weighting the soft reliability of the extrinsic information-sums based on their hard reliability, the proposed algorithms can achieve good error performance for non-binary LDPC codes with various column weights. Moreover, their computational complexity and memory consumption are remarkably reduced compared with existing MLgD based decoding algorithms. As a result, they provide effective tradeoffs between error performance and complexity for decoding of non-binary LDPC codes.

[1]  Xinmiao Zhang,et al.  Low-Complexity Reliability-Based Message-Passing Decoder Architectures for Non-Binary LDPC Codes , 2012, IEEE Transactions on Very Large Scale Integration (VLSI) Systems.

[2]  David J. C. MacKay,et al.  Low-density parity check codes over GF(q) , 1998, IEEE Communications Letters.

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

[4]  Zhiyuan Yan,et al.  Improved iterative soft-reliability-based majority-logic decoding algorithm for non-binary low-density parity-check codes , 2011, 2011 Conference Record of the Forty Fifth Asilomar Conference on Signals, Systems and Computers (ASILOMAR).

[5]  Shu Lin,et al.  Construction of nonbinary cyclic, quasi-cyclic and regular LDPC codes: a finite geometry approach , 2008, IEEE Transactions on Communications.

[6]  Zongwang Li,et al.  A Simplified Min-Sum Decoding Algorithm for Non-Binary LDPC Codes , 2012, IEEE Transactions on Communications.

[7]  Shu Lin,et al.  High Performance Nonbinary Quasi-Cyclic LDPC Codes on Euclidean Geometries , 2007, MILCOM 2007 - IEEE Military Communications Conference.

[8]  Henk Wymeersch,et al.  Log-domain decoding of LDPC codes over GF(q) , 2004, 2004 IEEE International Conference on Communications (IEEE Cat. No.04CH37577).

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

[10]  Shu Lin,et al.  Construction of non-binary quasi-cyclic LDPC codes by arrays and array dispersions - [transactions papers] , 2009, IEEE Transactions on Communications.

[11]  D. Declercq,et al.  Fast Decoding Algorithm for LDPC over GF(2q) , 2003 .

[12]  David J. C. MacKay,et al.  Good Codes Based on Very Sparse Matrices , 1995, IMACC.

[13]  David Declercq,et al.  Low-complexity decoding for non-binary LDPC codes in high order fields , 2010, IEEE Transactions on Communications.

[14]  Dan Feng Zhao,et al.  Min-Max decoding for non binary LDPC codes , 2016 .

[15]  Shu Lin,et al.  Construction of Quasi-Cyclic LDPC Codes for AWGN and Binary Erasure Channels: A Finite Field Approach , 2007, IEEE Transactions on Information Theory.

[16]  Noga Alon,et al.  A linear time erasure-resilient code with nearly optimal recovery , 1996, IEEE Trans. Inf. Theory.

[17]  David Declercq,et al.  Trellis-Based Extended Min-Sum Algorithm for Non-Binary LDPC Codes and its Hardware Structure , 2013, IEEE Transactions on Communications.

[18]  David Declercq,et al.  Trellis based Extended Min-Sum for decoding nonbinary LDPC codes , 2011, 2011 8th International Symposium on Wireless Communication Systems.

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

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