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Journal of Computer and Communications

Performance and Complexity Trade-Off between Short-Length Regular and Irregular LDPC

Ziyuan Peng, Ruizhe Yang

Published Jan 1, 2024• 1 citation
Publisher

Abstract

In this paper, both the high-complexity near-ML list decoding and the low-complexity belief propagation decoding are tested for some well-known regular and irregular LDPC codes. The complexity and performance trade-off is shown clearly and demonstrated with the paradigm of hybrid decoding. For regular LDPC code, the SNR-threshold performance and error-floor performance could be improved to the optimal level of ML decoding if the decoding complexity is progressively increased, usually corresponding to the near-ML decoding with progressively increased size of list. For irregular LDPC code, the SNR-threshold performance and error-floor performance could only be improved to a bottle-neck even with unlimited decoding complexity. However, with the technique of CRC-aided hybrid decoding, the ML performance could be greatly improved and approached with reasonable complexity thanks to the improved code-weight distribution from the concatenation of CRC and irregular LDPC code. Finally, CRC-aided 5GNR-LDPC code is evaluated and the capacity-approaching capability is shown.

DOI
10.4236/jcc.2024.129012

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In this paper, both the high-complexity near-ML list decoding and the low-complexity belief propagation decoding are tested for some well-known regular and irregular LDPC codes. The complexity and performance trade-off is shown clearly and demonstrated with the paradigm of hybrid decoding. For regular LDPC code, the SNR-threshold performance and error-floor performance could be improved to the optimal level of ML decoding if the decoding complexity is progressively increased, usually corresponding to the near-ML decoding with progressively increased size of list. For irregular LDPC code, the SNR-threshold performance and error-floor performance could only be improved to a bottle-neck even with unlimited decoding complexity. However, with the technique of CRC-aided hybrid decoding, the ML performance could be greatly improved and approached with reasonable complexity thanks to the improved code-weight distribution from the concatenation of CRC and irregular LDPC code. Finally, CRC-aided 5GNR-LDPC code is evaluated and the capacity-approaching capability is shown.
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This paper investigates about the usefulness of some recently published low complexity upper bounds on belief-propagation decoding thresholds for irregular low-density parity-check (LDPC) codes to analyze their performance on memoryless binary input - additive white Gaussian noise (BI-AWGN) channels, with sum-product decoding. Irregular LDPC codes are known to perform better than regular ones, and to exhibit, like them, the so called “threshold phenomenon”, being the threshold defined as the maximum noise level such that an arbitrarily small bit-error probability can be achieved as the block length tends to infinity. We use a simplified analysis of the belief-propagation decoding algorithm, i.e., consider a Gaussian approximation for message densities under density evolution, and a simple algorithmic method, defined recently, to estimate the decoding thresholds for regular and irregular LDPC codes on BI-AWGN channels.
LDPC code shows a good performance with long-block codes. However, certain channels are constrained to use short-block codes due to latency. Therefore, concatenated LDPC codes with iterative decoding is a good choice to get a good performance. Concatenated binary LDPC codes were introduced as a class of concatenated codes in which the LDPC codes are irregular codes having different parameters. Although irregular LDPC codes are more efficient than regular codes, irregular LDPC codes have an error floor and a higher encoding complexity than regular code. In this paper, in order to get a good performance/complexity trade-off with a short-block code, we investigate a parallel concatenation of two identical regular binary LDPC codes, using an interleaver. Simulation results show that the proposed code outperforms a single LDPC code. The proposed code needs less time decoding delay than a single LDPC code with the same iteration number. Also, the proposed code needs a less number of iterations to achieve the same performance of a single LDPC code that leads to less decoding complexity and decoding delay. A simplified algorithm, the min-sum algorithm, that is used to decode the component codes shows a small performance loss with respect to the sum-product algorithm.
In this paper, we derive an upper bound for the average block error probability of a standard irregular low-density parity-check (LDPC) code ensemble under the maximum-likelihood (ML) decoding. Moreover, we show that the upper bound asymptotically decreases polynomially with the code length. Furthermore, when we consider several regular LDPC code ensembles as special cases of standard irregular ones over an additive white Gaussian noise channel, we numerically show that the signal-to-noise ratio (SNR) thresholds at which the proposed bound converges to zero as the code length tends to infinity are smaller than those for a bound provided by Miller et al. We also give an example of a standard irregular LDPC code ensemble which has a lower SNR threshold than a given regular LDPC code ensemble.
The performance of maximum-likelihood (ML) decoding on the binary erasure channel for finite-length low-density parity-check (LDPC) codes from two random ensembles is studied. A tightened union-type upper bound on the ML decoding error probability based on the precise coefficients of the average weight spectrum is presented. For LDPC codes from the Gallager ensemble and the Richardson-Urbanke ensemble, new upper bounds on the ML decoding performance based on computing the rank of submatrices of the code parity-check matrix are derived. A new lower bound on the ML decoding threshold followed from the latter error probability bound is obtained. An improved lower bound on the error probability for codes with a known estimate on the minimum distance is presented as well. A new low-complexity near-ML decoding algorithm for quasi-cyclic LDPC codes is proposed and simulated. Its performance is compared to the simulated belief propagation and ML decoding performance and simulated performance of the best known improved iterative decoding techniques, as well as, with the derived upper bounds on the ML decoding performance and with decoding thresholds obtained by the density evolution technique.
Low-Density Parity-Check (LDPC) codes have been widely used in modern communication standards due to their strong error correction capabilities. This paper presents an experimental evaluation of a (1200, 600) irregular LDPC code over an additive white Gaussian noise (AWGN) channel, systematically comparing three decoding algorithms (Sum-Product, Normalized Min-Sum, and Offset Min-Sum) with three scheduling methods (Flooding, Layered Belief Propagation, and Residual Belief Propagation). Parameter sweeps are performed to determine the optimal normalization factor (α\alphaα) for the Normalized Min-Sum and the offset factor (β\betaβ) for the Offset Min-Sum. A comparative analysis is then performed on the frame error rate (FER) and convergence behavior of each algorithm and scheduling configuration, considering the maximum number of iterations set at 10 and 25. The results show that the Offset Min-Sum algorithm withβ=0.5\beta=0.5β=0.5and Layered Belief Propagation scheduling provides an acceptable trade-off between complexity and error-correction performance, closely matching the Sum-Product algorithm but at a lower computational cost. Although Residual Belief Propagation converges quickly at lower signal-to-noise ratios, it exhibits a high error floor. These findings provide practical guidelines for selecting optimal decoding configurations in resource-constrained applications.