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

Dolecek, Lara; Divsalar, D.; Sun, Yizeng; Amiri, Behzad

doi:10.1109/tit.2014.2316215

Cited by 88 publications

(76 citation statements)

References 57 publications

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“…Beyond that, a variety of simple but sub-optimal decoding algorithms have been proposed in the literature, such as the extended min-sum (EMS) algorithm [3] and the trellisbased EMS algorithm [4]. For computing iterative BP decoding thresholds, a q-ary extrinsic information transfer (EXIT) analysis was proposed in [5] and was later developed into a version suitable for protograph-based code ensembles in [6].…”

Section: Index Termsmentioning

confidence: 99%

“…2) For the binary-input additive white Gaussian noise channel (BIAWGNC) with binary phaseshift keying (BPSK) modulation, we obtain windowed decoding thresholds for q-ary SC-LDPC code ensembles by applying a protograph-based EXIT analysis (originally proposed for q-ary LDPC-BC ensembles [6]) in conjunction with WD.…”

Section: Index Termsmentioning

confidence: 99%

“…For example, for an arbitrary m, let (J, K) = (3,6). In this case k = 2, and we consider the "classical" edge spreading with w = J − 1 = 2 along with k + 1 = 3 types of edge spreading with w = 1, viz.…”

Section: Code Ensemble Constructionmentioning

confidence: 99%

“…Similar to the procedure used to extend q-ary EXIT analysis to a protograph version in [6], we now extend the q-ary DE algorithm to a protograph version, which we refer to as q-ary protograph DE (PDE). Since the edge connections are taken into account and the computation graph is equal for all members of the ensemble, PDE reduces to the BP algorithm performed on the protograph.…”

Section: A Protograph Density Evolution (De) For Q-ary Ldpc Code Ensmentioning

confidence: 99%

“…Since the edge connections are taken into account and the computation graph is equal for all members of the ensemble, PDE reduces to the BP algorithm performed on the protograph. We use notation similar to that in [6] and [28]. Let b i,j denote a non-zero entry in the base matrix and recall that, from the perspective of the protograph, the value of b i,j is the number of edges connecting check node i (the row index in the matrix) to variable node j (the column index), rather than an edge label.…”

Section: A Protograph Density Evolution (De) For Q-ary Ldpc Code Ensmentioning

confidence: 99%

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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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Section: Index Termsmentioning

confidence: 99%

Section: Index Termsmentioning

confidence: 99%

Section: Code Ensemble Constructionmentioning

confidence: 99%

Section: A Protograph Density Evolution (De) For Q-ary Ldpc Code Ensmentioning

confidence: 99%

Section: A Protograph Density Evolution (De) For Q-ary Ldpc Code Ensmentioning

confidence: 99%

See 3 more Smart Citations

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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Low‐Density Parity‐Check ( LDPC ) Codes for 5G Communications

2021

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In this article, we describe the fundamental advances in low‐density parity‐check (LDPC) codes over the last two decades with special emphasis on the class of LDPC codes selected for the 5G new radio standard. We present structured protograph and quasi‐cyclic LDPC codes, which are convenient for hardware implementation. The 5G LDPC codes are then reviewed in detail. Hardware considerations regarding the implementation of the encoders and decoders of 5G LDPC codes are also discussed. We conclude the article by presenting three of the more promising extensions of LDPC codes known to date (generalized LDPC codes, nonbinary LDPC codes, and spatially coupled LDPC codes), which could potentially replace conventional LDPC codes in future communication standards.

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