Non-Binary Protograph-Based LDPC Codes: Enumerators, Analysis, and Designs

被引:69
作者
Dolecek, Lara [1 ]
Divsalar, Dariush [2 ]
Sun, Yizeng [1 ]
Amiri, Behzad [1 ]
机构
[1] Univ Calif Los Angeles, Dept Elect Engn, Los Angeles, CA 90095 USA
[2] CALTECH, Jet Prop Lab, Pasadena, CA 91109 USA
基金
美国国家科学基金会; 美国国家航空航天局;
关键词
LDPC codes; nonbinary codes; protographs; weight enumerators; asymptotic analysis; pseudo-codewords; trapping sets; stopping sets; iterative decoding thresholds; EXIT chart analysis; finite-length code design; PARITY-CHECK CODES; MINIMUM DISTANCE; WEIGHT; BINARY;
D O I
10.1109/TIT.2014.2316215
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
This paper provides a comprehensive analysis of nonbinary low-density parity check (LDPC) codes built out of protographs. We consider both random and constrained edge-weight labeling, and refer to the former as the unconstrained nonbinary protograph-based LDPC codes (U-NBPB codes) and to the latter as the constrained nonbinary protograph-based LDPC codes (C-NBPB codes). Equipped with combinatorial definitions extended to the nonbinary domain, ensemble enumerators of codewords, trapping sets, stopping sets, and pseudocodewords are calculated. The exact enumerators are presented in the finite-length regime, and the corresponding growth rates are calculated in the asymptotic regime. An EXIT chart tool for computing the iterative decoding thresholds of protograph-based LDPC codes is presented, followed by several examples of finite-length U-NBPB and C-NBPB codes with high performance. Throughout this paper, we provide accompanying examples, which demonstrate the advantage of nonbinary protograph-based LDPC codes over their binary counterparts and over random constructions. The results presented in this paper advance the analytical toolbox of nonbinary graph-based codes.
引用
收藏
页码:3913 / 3941
页数:29
相关论文
共 62 条
[1]   Accumulate-repeat-accumulate codes [J].
Abbasfar, Aliazam ;
Divsalar, Dariush ;
Yao, Kung .
IEEE TRANSACTIONS ON COMMUNICATIONS, 2007, 55 (04) :692-702
[2]  
Abu-Surra S., 2009, P IEEE GLOB TEL C HO, P1
[3]   Enumerators for Protograph-Based Ensembles of LDPC and Generalized LDPC Codes [J].
Abu-Surra, Shadi ;
Divsalar, Dariush ;
Ryan, William E. .
IEEE TRANSACTIONS ON INFORMATION THEORY, 2011, 57 (02) :858-886
[4]   Finite-Length Scaling of Non-Binary (c, d) LDPC Codes for the BEC [J].
Andriyanova, Iryna ;
Kasai, Kenta .
2010 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY, 2010, :714-718
[5]   Binary Weight Distribution of Non-Binary LDPC Codes [J].
Andriyanova, Iryna ;
Rathi, Vishwambhar ;
Tillich, Jean-Pierre .
2009 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY, VOLS 1- 4, 2009, :65-69
[6]  
[Anonymous], 2006, Elements of Information Theory
[7]  
[Anonymous], [No title captured]
[8]  
[Anonymous], 2008, UPL COD NEW IN PRESS
[9]  
[Anonymous], 1963, Low-Density Parity-Check Codes
[10]  
Barnault L, 2003, 2003 IEEE INFORMATION THEORY WORKSHOP, PROCEEDINGS, P70