Analysis of error floors of generalized non-binary LDPC codes over q-ary memoryless symmetric channels

Nozaki, Takayuki; Kasai, Kazuhiko; Sakaniwa, Kohichi

doi:10.1109/isit.2012.6283931

Cited by 4 publications

(6 citation statements)

References 8 publications

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“…Codes with efficient encoding and decoding were proposed in [52]. The error-floor performance of non-binary LDPC codes was recently investigated in [36] and [38], and non-codeword objects that cause the decoding error under iterative decoding were studied in [37] and [41]. Minimum distance properties of non-binary LDPC codes were recently explored in [29].…”

Section: Introductionmentioning

confidence: 99%

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

Dolecek

Divsalar

Sun

et al. 2014

IEEE Trans. Inform. Theory

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Abstract-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, 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. 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.

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Section: Introductionmentioning

confidence: 99%

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

Dolecek

Divsalar

Sun

et al. 2014

IEEE Trans. Inform. Theory

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“…Since every permutation of the columns of B Cp results in same determinant, the chosen ordering was performed without loss of generality. It can be shown that if the cycle span satisfies (5), this also holds for all other cycles in the graph. Thus, a subgraph of the Tanner graph is an elementary NB-AS if it satisfies the topological conditions, i.e., the unlabeled subgraph satisfies the conditions of an elementary binary ASs, and all of its fundamental cycles satisfy (5).…”

Section: Non-binary Absorbing Setsmentioning

confidence: 99%

“…For each of the remaining e−(a−1) edges in the VN graph that are not in the spanning tree, one of the two edges in the Tanner graph can again be chosen arbitrarily but the other edge is uniquely determined according to (5). Thus, there are (q − 1) e−a+1 weight assignments for edges not in the spanning tree.…”

Section: Asymptotic Distribution Of Nb-as In Regular Code Ensemblesmentioning

confidence: 99%

“…Important recent results include stopping constellation distributions for irregular NB-LDPC code ensembles [3], as well as the analysis of zig-zag cycles and their relationship with the error floor [4], [5]. Further, ensemble enumerators for stopping set and This work was supported in part by NSF grants CCF-0830666, CCF-1161774, and CCF-1161798. trapping set sizes are found in [6] for protograph-based ensembles of NB-LDPC codes.…”

Section: Introductionmentioning

confidence: 99%

“…Table I includes the error profile for all three codes over GF (4). Both P-method and A-method eliminate all (4, 4) ASs as well as (5, 0), (5,2), (6,2) and (6,4) ASs that are children of (4, 4) ASs. Additionally, A-method successfully eliminates all (6, 6), (7,4) and (8, 2) ASs since in this approach, we selectively cancel some (but not necessary all) length 6 cycles followed by cancellation of some of length 8 cycles.…”

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confidence: 99%

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Analysis and enumeration of absorbing sets for non-binary graph-based codes

Amiri

Kliewer

Dolecek

2013

2013 IEEE International Symposium on Information Theory

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This work provides a generalization of absorbing sets for linear channel codes over non-binary alphabets. In a graphical representation of a non-binary channel code, an absorbing set can be described by a collection of topological and edge labeling conditions. In the non-binary case the equations relating neighboring variable and check nodes are over a nonbinary field, and the edge weights are given by the non-zero elements of that non-binary field. As a consequence, it becomes more difficult for a given structure to satisfy the absorbing set constraints. This observation in part explains the superior performance of non-binary codes over their binary counterparts. We first show that, as the field order size increases, the ratio of trapping sets that satisfy the structural conditions of absorbing sets decreases. This suggests that a trapping set-only performance estimation of non-binary codes may not be as accurate in the error floor/high reliability regime. By using both insights from graph theory and combinatorial techniques, we establish the asymptotic distribution of non-binary elementary absorbing sets for regular code ensembles. Finally, we provide design guidelines for finite-length non-binary codes free of small absorbing sets.

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