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

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Bibliographic Details
Title: Non-Binary Protograph-Based LDPC Codes: Enumerators, Analysis, and Designs.
Authors: Dolecek, Lara, Divsalar, Dariush, Sun, Yizeng, Amiri, Behzad
Source: IEEE Transactions on Information Theory; Jul2014, Vol. 60 Issue 7, p3913-3941, 29p
Subject Terms: ITERATIVE decoding, COMBINATORICS, LOW density parity check codes, OPTICAL communications, ENUMERATIVE coding
Abstract: 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. [ABSTRACT FROM AUTHOR]
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Abstract: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. [ABSTRACT FROM AUTHOR]
ISSN:00189448
DOI:10.1109/TIT.2014.2316215