Protograph LDPC Codes Design Based on EXIT Analysis

Liva, Gianluigi; Chiani, Marco

doi:10.1109/glocom.2007.616

Cited by 257 publications

(243 citation statements)

References 8 publications

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“…In particular, the method is designed to efficiently evaluate thresholds of U-NBPB codes and generalizes the EXIT-chart methodology previously developed for binary protograph-based codes in [30] and for unstructured non-binary LDPC codes in [5]. We call the proposed technique non-binary PEXIT (NB-PEXIT).…”

Section: Iterative Thresholds Via Exit Charts For Non-binary Protmentioning

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: Iterative Thresholds Via Exit Charts For Non-binary Protmentioning

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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“…Although some freedom is lost in the code design when the protograph structure is adopted, one can use these modified protograph-based analysis tools to find "good" protograph-based ensembles with better BP thresholds than corresponding unstructured ensembles with the same degree distribution [10], [11].…”

Section: Index Termsmentioning

confidence: 99%

Design of Spatially Coupled LDPC Codes Over GF $(q)$ for Windowed Decoding

Wei

Mitchell

Fuja

et al. 2016

IEEE Trans. Inform. Theory

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In this paper we consider the generalization of binary spatially coupled low-density parity-check (SC-LDPC) codes to finite fields GF(q), q ≥ 2, and develop design rules for q-ary SC-LDPC code ensembles based on their iterative belief propagation (BP) decoding thresholds, with particular emphasis on low-latency windowed decoding (WD). We consider transmission over both the binary erasure channel (BEC) and the binary-input additive white Gaussian noise channel (BIAWGNC) and present results for a variety of (J, K)-regular SC-LDPC code ensembles constructed over GF(q) using protographs.Thresholds are calculated using protograph versions of q-ary density evolution (for the BEC) and qary extrinsic information transfer analysis (for the BIAWGNC). We show that WD of q-ary SC-LDPC codes provides significant threshold gains compared to corresponding (uncoupled) q-ary LDPC block code (LDPC-BC) ensembles when the window size W is large enough and that these gains increase as the finite field size q = 2 m increases. Moreover, we demonstrate that the new design rules provide WD thresholds that are close to capacity, even when both m and W are relatively small (thereby reducing decoding complexity and latency). The analysis further shows that, compared to standard flooding-schedule decoding, WD of q-ary SC-LDPC code ensembles results in significant reductions in both decoding complexity and decoding latency, and that these reductions increase as m increases.For applications with a near-threshold performance requirement and a constraint on decoding latency, we show that using q-ary SC-LDPC code ensembles, with moderate q > 2, instead of their binary counterparts results in reduced decoding complexity.

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“…I. Table. II gives the decoding thresholds of the constructed HRSEV codes. The decoding thresholds were computed by PEXIT charts [10], showing that the gaps to capacity between 0.22 dB and 0.26 dB have been achieved. Simulations were also carried out to evaluate the performance of the obtained HRSEV codes.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…As a result, we mainly focus on the performance in water-fall regions, which can be efficiently evaluated by the decoding threshold using PEXIT charts analysis [10]. Generally, a decoding threshold with gap to capacity less than 0.25dB is already a good result.…”

Section: B Improved Multiple-rate Qc-ldpc Codes Constructionmentioning

confidence: 99%

“…However, the general EXIT charts cannot be applied to compute the decoding thresholds of QC-LDPC codes with the same degree distribution. Thus we adopt the PEXIT method proposed in [10] to compute the thresholds of QC-LDPC codes with certain base matrices. The decoding threshold is defined as the minimum channel quality that supports reliable decoding when the blocklength is asymptotically large.…”

Section: Introductionmentioning

confidence: 99%

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Construction of Multiple-Rate QC-LDPC Codes Using Hierarchical Row-Splitting

Zhao

Wang

2016

IEEE Commun. Lett.

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Abstract-In this letter, we propose an improved method called hierarchical row-splitting with edge variation for designing multiple-rate quasi-cyclic low-density parity-check (QC-LDPC) codes, which constructs lower-rate codes from a high-rate mother code by row-splitting operations. Consequently, the obtained QC-LDPC codes with various code rates have the same blocklength and can share common hardware resources to reduce the implementation complexity. Compared with the conventional row-combining-based algorithms, a wider range of code rates are supported. Moreover, each individual rate code could be separately optimized, making it easier to find a set of multiplerate QC-LDPC codes with good performance for all different rates. Simulation results demonstrate that the obtained codes outperform the counterparts from digital video broadcastingsecond generation terrestrial.

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Protograph LDPC Codes Design Based on EXIT Analysis

Cited by 257 publications

References 8 publications

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

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

Design of Spatially Coupled LDPC Codes Over GF $(q)$ for Windowed Decoding

Construction of Multiple-Rate QC-LDPC Codes Using Hierarchical Row-Splitting

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