一种简化的GF(q)-LDPC码译码算法

doi:10.3969/j.issn.1001-2400.2011.02.002

Abstract

Abstract:

A simple, yet effective decoding algorithm for LDPC (low-density parity-check) codes over GF(q) is presented. By taking advantages of the first-term Taylor's series expansion to approximate the correction term of the Jacobian logarithm used in LLR-SPA(log-likelihood ratio sum-product algorithm), we propose an algorithm which significantly simplifies the check node update computation of the optimal LLR-SPA. Compared to the offset min-sum algorithm, the proposed algorithm achieves a gain of about 0.2dB at the BER of 10^-4. Moreover, unlike the offset min-sum algorithm, parameters of this algorithm are independent of the order of the Galois Filed.

Key words: nonbinary LDPC codes, sum-product algorithm, min-sum algorithm, iterative decoding

HU Shukai;WANG Xinmei. Simplified decoding algorithm for LDPC over GF(q)[J].J4, 2011, 38(2): 8-12+196.

References

［1］ Gallager R G. Low Density Parity-check Codes［D］. Cambridge: MIT Press, 1963.
［2］ Chung S, Jr Forney G D, Richardson T J, et al. On the Design of Low-density Parity-check Codes within 0.0045dB of the Shannon Limit［J］. IEEE Communications Letters, 2001, 5(2): 58-60.
［3］ Davey M C, Mackay D J C. Low Density Parity Check Codes over GF(q)［C］//Proceedings of 1998 Information Theory Workshop. San Diego: IEEE, 1998: 70-71.
［4］ Kschischang F R, Frey B J, Loeliger H A. Factor Graphs and the Sum-product Algorithm［J］. IEEE Trans on Information Theory, 2001, 47(2): 498-519.
［5］童胜, 王鹏, 王单, 等. LDPC码量化和积译码的高效实现［J］. 西安电子科技大学学报, 2004, 31(5): 709-713.
Tong Sheng, Wang Peng, Wang Dan, et al. Efficient Implementation of the Sum-product Algorithm for Quantized Decoding of LDPC Codes［J］. Journal of Xidian University, 2004, 31(5): 709-713.
［6］ Chen J, Dholakia A, Eleftheriou E, et al. Reduced-complexity Decoding of LDPC Codes［J］. IEEEJCOM, 2005, 53(8): 1288-1299.
［7］ Liao C H, Wang C Y, Liu C H, et al. An O(qlogq) Log-domain Decoder for Non-binary LDPC over GF(q)［C］//Proceedings of 2008 Asia Pacific Conference on Circuits and Systems. Macao: IEEE, 2008: 1644-1647.
［8］ Declercq D, Fossorier M. Decoding Algorithms for Nonbinary LDPC Codes Over GF(q)［J］. IEEE Trans on Communications, 2007, 55(4): 633-643.
［9］ Boutillon E, Conde-Canencia L. Bubble Check: a Simplified Algorithm for Elementary Check Node Processing in Extended Min-sum Non-binary LDPC Decoders［J］. Electronics Letters, 2010, 46(9): 633-634.
［10］ Li P, Leung W K, Wu K Y. Low-rate Turbo-Hadamard Codes［J］. IEEE Transactions on Information Theory, 2003, 49(12): 3213-3224.
［11］ Wymeersch H, Steendam H, Moeneclaey M. Log-domain Decoding of LDPC Codes over GF(q)［C］//Proceedings of 2004 International Conference on Communications. Paris: IEEE, 2004: 772-776.
［12］ Talakoub S, Sabeti L, Shahrrava B, et al. An Improved Max-log-MAP Algorithm for Turbo Decoding and Turbo Equalization［J］. IEEE Trans on Instrumentation and Measurement, 2007, 56(3): 1058-1063.
［13］ Papaharalabos S, Mathiopoulos P T. Simplified Sum-product Algorithm for Decoding LDPC Codes with Optimal Performance［J］. Electronics Letters, 2009, 45(2): 116-117.

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Simplified decoding algorithm for LDPC over GF(q)

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