循环差族构造的多元LDPC码

doi:10.3969/j.issn.1001-2400.2017.01.002

摘要/Abstract

摘要：

基于循环差族构造了两类多元低密度奇偶校验码，并提出了不同有限域上各个码率的多元低密度奇偶校验码的构造方法．所构造的多元低密度奇偶校验环码(校验矩阵的列重均为2)的围长为12，同时证明了该类码的最小距离至少为6．仿真结果表明，所构造的多元低密度奇偶校验码与用其他方法构造的二元及多元低密度奇偶校验码相比，在加性高斯白噪声信道上二进制相移键控调制下均有性能提升，并且迭代译码收敛速度非常快．

关键词: 低密度奇偶校验码, 多元, 准循环, 循环差族, 围长

Abstract:

This paper presents two classes of nonbinary LDPC codes based on cyclic difference families. A method of constructing nonbinary LDPC codes with various rates and over different fields is also proposed. A class of codes whose parity-check matrices consist of weight-2 columns, known as cycle codes, has girth 12, and it is also proved that these codes have a minimum distance of at least 6. Simulation results show that the constructed nonbinary LDPC codes outperform the binary and nonbinary codes derived from other constructions over the AWGN channel with BPSK modulation.

Key words: low-density parity-check (LDPC) codes, nonbinary, quasi-cyclic (QC), cyclic difference families, girth

徐恒舟;孙成;白宝明. 循环差族构造的多元LDPC码[J]. 西安电子科技大学学报, 2017, 44(1): 6-11+28.

XU Hengzhou;SUN Cheng;BAI Baoming. Nonbinary LDPC codes constructed based on cyclic difference families[J]. Journal of Xidian University, 2017, 44(1): 6-11+28.

参考文献

［1］ GALLAGER R G. Low-density Parity-check Codes ［J］. IRE Transactions on Information Theory, 1962, 8(1): 21-28.
［2］ DAVEY M C, MACKAY D J C. Low Density Parity Check Codes over GF(q) ［C］//Proceedings of the 1998 Information Theory Workshop. New York: IEEE,1998: 70-71.
［3］ ZHU M, GUO Q, BAI B M, et al. Reliability-based Joint Detection-decoding Algorithm for Nonbinary LDPC-coded Modulation Systems ［J］. IEEE Transactions on Communications, 2016, 64(1): 2-14.
［4］ SONG L Y, HUANG Q, WANG Z L, et al. Two Enhanced Reliability-based Decoding Algorithms for Nonbinary LDPC Codes ［J］. IEEE Transactions on Communications, 2016, 64(2): 479-489.
［5］ POULLIAT C, FOSSORIER M, DECLERCQ D. Design of Regular (2, dc)-LDPC Codes over GF(q) Using Their Binary Images ［J］. IEEE Transactions on Communications, 2008, 56(10): 1626-1635.
［6］ DIAO Q J, TAI Y Y, LIN S, et al. LDPC Codes on Partial Geometries: Construction, Trapping Set Structure, and Puncturing ［J］. IEEE Transactions on Information Theory, 2013, 59(12): 7898-7914.
［7］ LI J, LIU K, LIN S, et al. Algebraic Quasi-cyclic LDPC Codes: Construction, Low Error-floor, Large Girth and a Reduced-complexity Decoding Scheme ［J］. IEEE Transactions on Communications, 2014, 62(8): 2626-2637.
［8］ ZHAO S C, MA X, ZHANG X Y, et al. A Class of Nonbinary LDPC Codes with Fast Encoding and Decoding Algorithms ［J］. IEEE Transactions on Communications, 2013, 61(1): 1-6.
［9］ DOLECEK L, DIVSALAR D, SUN Y, et al. Non-binary Protograph-based LDPC Codes: Enumerators, Analysis, and Designs ［J］. IEEE Transactions on Information Theory, 2014, 60(7): 3913-3941.
［10］ CHEN C, BAI B M, SHI G M, et al. Nonbinary LDPC Codes on Cages: Structural Property and Code Optimization ［J］. IEEE Transactions on Communications, 2015, 63(2): 364-375.
［11］沈灏. 组合设计理论［M］. 上海: 上海交通大学出版社, 2008: 92-124.
［12］ PARK H, HONG S, NO J S, et al. Construction of High-rate Regular Quasi-cyclic LDPC Codes Based on Cyclic Difference Families ［J］. IEEE Transactions on Communications, 2013, 61(8): 3108-3113.
［13］ ZHAO X, ZHANG L J, CHENG L. Construction of Nonbinary LDPC Codes: Prime Difference Approach ［C］//IET Conference Publications: 2011. Stevenage: IET, 2011: 114-117.
［14］ RYAN W E, LIN S. Channel Codes: Classical and Modern ［M］. New York: Cambridge University Press, 2009: 593-600.
［15］ COLBOURN C J, DINITZ J. The CRC Handbook of Combinatorial Designs ［M］. 2nd Edition. Boca Raton: CRC Press, 2006: 392-410.
［16］ FOSSORIER M. Quasi-cyclic Low-density Parity-check Codes from Circulant Permutation Matrices ［J］. IEEE Transactions on Information Theory, 2004, 50(8): 1788-1793.
［17］ CHEN C, BAI B M, WANG X M. Construction of Nonbinary Quasi-cyclic LDPC Cycle Codes Based on Singer Perfect Difference Set ［J］. IEEE Communications Letters, 2010, 14(2): 181-183.
［18］ HU X Y, ELEFTHERIOU E, ARNOLD D M. Regular and Irregular Progressive Edge-growth Tanner Graphs ［J］. IEEE Transactions on Information Theory, 2005, 51(1): 386-398.
［19］林伟. 多元LDPC码:设计、构造与译码［D］. 西安: 西安电子科技大学, 2012.
［20］ IEEE Standards Association. IEEE Standard for Local and Metropolitan Area Networks. Part 16: Air Interface for Fixed and Mobile Broadband Wireless Access Systems: IEEE 802.16e-2006 ［S］. New York: IEEE, 2006.
［21］ CCSDS. Short Block Length LDPC Codes for TC Synchronization and Channel Coding, Research and Development for Space Data System Standards: CCSDS 231.1-O-1［S］. Washington: CCSDS, 2015.
［22］ SONG L Y, ZHANG M, HUANG Q, et al. Low Error-floor Majority-logic Decoding Based Algorithm for Non-binary LDPC Codes ［C］//Proceedings of the IEEE International Conference on Communications: 2015. Piscataway: IEEE, 2015: 4072-4076.
［23］ POLYANSKIY Y, POOR H V, VERDU S, Channel Coding Rate in the Finite Block Length Regime ［J］. IEEE Transactions on Information Theory, 2010, 56(5): 2307-2359.

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