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

Lara Dolecek, Dariush Divsalar, Yizeng Sun, Behzad Amiri
2014 IEEE Transactions on Information Theory  
This paper provides a comprehensive analysis of non-binary low-density parity check (LDPC) codes built out of protographs. We consider both random and constrained edgeweight labeling, and refer to the former as the unconstrained non-binary protograph-based LDPC codes (U-NBPB codes) and the latter as the constrained non-binary protograph-based LDPC codes (C-NBPB codes). Equipped with combinatorial definitions extended to the non-binary domain, ensemble enumerators of codewords, trapping sets,
more » ... pping 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. We then present an EXIT chat tool for computing the iterative decoding thresholds of protograph-based LDPC codes followed by several examples of finite-length U-NBPB and C-NBPB codes with high performance. Throughout the paper, we provide accompanying examples which demonstrate the advantage of non-binary protograph-based LDPC codes over their binary counterparts and over random constructions. The results presented in this paper advance the analytical toolbox of non-binary graph-based codes.
doi:10.1109/tit.2014.2316215 fatcat:72qisp7jn5abrghxtg2fkaihwy