A Unified Approach to the Construction of Binary and Nonbinary Quasi-Cyclic LDPC Codes Based on Finite Fields

被引:77
作者
Song, Shumei [1 ]
Zbou, Bo [1 ]
Lin, Shu [1 ]
Abdel-Ghaffar, Khaled [1 ]
机构
[1] Univ Calif Davis, Dept Elect & Comp Engn, Davis, CA 95616 USA
基金
美国国家科学基金会; 美国国家航空航天局;
关键词
Base matrix; dispersion; finite field; LDPC codes; location-vector; quasi-cyclic; PARITY-CHECK CODES; REED-SOLOMON CODES; MATRICES; CHANNELS; CAPACITY; DESIGN;
D O I
10.1109/TCOMM.2009.0901.060129
中图分类号
TM [电工技术]; TN [电子技术、通信技术];
学科分类号
0808 ; 0809 ;
摘要
A unified approach for constructing binary and nonbinary quasi-cyclic LDPC codes under a single framework is presented. Six classes of binary and nonbinary quasi-cyclic LDPC codes are constructed based on primitive elements, additive subgroups, and cyclic subgroups of finite fields. Numerical results show that the codes constructed perform well over the AWGN channel with iterative decoding.
引用
收藏
页码:84 / 93
页数:10
相关论文
共 33 条
[1]  
[Anonymous], 1958, An Introduction to Combinatorial Analysis
[2]  
Barnault L, 2003, 2003 IEEE INFORMATION THEORY WORKSHOP, PROCEEDINGS, P70
[3]   Design and analysis of nonbinary LDPC codes for arbitrary discrete-memoryless channels [J].
Bennatan, A ;
Burshtein, D .
IEEE TRANSACTIONS ON INFORMATION THEORY, 2006, 52 (02) :549-583
[4]  
Berlekamp E. R., 2015, ALGEBRAIC CODING THE
[5]   Near-Shannon-limit quasi-cyclic low-density parity-check codes [J].
Chen, L ;
Xu, J ;
Djurdjevic, I ;
Lin, S .
IEEE TRANSACTIONS ON COMMUNICATIONS, 2004, 52 (07) :1038-1042
[6]   Analysis of sum-product decoding of low-density parity-check codes using a Gaussian approximation [J].
Chung, SY ;
Richardson, TJ ;
Urbanke, RL .
IEEE TRANSACTIONS ON INFORMATION THEORY, 2001, 47 (02) :657-670
[7]   Low-Density Parity Check Codes over GF (q) [J].
Davey, Matthew C. ;
MacKay, David .
IEEE COMMUNICATIONS LETTERS, 1998, 2 (06) :165-167
[8]   Decoding algorithms for nonbinary LDPC codes over GF(q) [J].
Declercq, David ;
Fossorier, Marc .
IEEE TRANSACTIONS ON COMMUNICATIONS, 2007, 55 (04) :633-643
[9]   Iterative algebraic soft-decision list decoding of Reed-Solomon codes [J].
El-Khamy, M ;
McEliece, RJ .
IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, 2006, 24 (03) :481-490
[10]   Quasi-cyclic low-density parity-check codes from circulant permutation matrices [J].
Fossorier, MPC .
IEEE TRANSACTIONS ON INFORMATION THEORY, 2004, 50 (08) :1788-1793