Efficient QP-ADMM Decoder for Binary LDPC Codes and Its Performance Analysis

Bai, Jian; Wang, Yongchao; Shi, Qingjiang

doi:10.1109/tsp.2020.2964223

Cited by 16 publications

(9 citation statements)

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“…Fig. 4 shows that the average iteration numbers required to realize decoding are comparable between the proposed proximal-ADMM decoder and the ADMM-PD methods [26] [27]. At last, we should also note that the proposed proximal-ADMM decoder is more efficient than the ADMM-PD decoder [26] since it eliminates time-consuming checkpolytope projections.…”

Section: A Performance Of the Proposed Proximal-admm Decodermentioning

confidence: 79%

“…Authors in [23]- [25] designed different cut-generating algorithms to eliminate unexpected pseudo-codewords and improve the error correction performance of LP decoding. In addition, authors in [26] and [27] independently proposed improved ADMM-based penalized decoding algorithms to enhance the error correction performance of LP decoding in low SNR regions.…”

Section: Introductionmentioning

confidence: 99%

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Proximal-ADMM Decoder for Nonbinary LDPC Codes

Wang,

Bai

2020

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In this paper, we develop an efficient decoder via the proximal alternating direction method of multipliers (proximal-ADMM) technique for nonbinary linear block codes in the Galois field. Its main contents are as follows: first, exploiting the decomposition technique based on the three-variables check equation, we formulate the maximum likelihood (ML) decoding problem approximately to a non-convex quadratic program; second, an efficient algorithm based on the proximal-ADMM technique is proposed to solve the formulated QP problem. Exploiting the QP problem's inherent structures, its variables can be updated in parallel; third, we prove that the proposed decoding algorithm can converge to some stationary point of the formulated QP problem. Moreover, we also show, for nonbinary low-density parity-check (LDPC) codes, its computational complexity in each proximal-ADMM iteration scales linearly with block length and the size of the considered Galois field. Simulation results demonstrate that the proposed proximal-ADMM decoder outperforms state-of-the-art nonbinary LDPC decoders in terms of either error correction performance or computational complexity.

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Section: A Performance Of the Proposed Proximal-admm Decodermentioning

confidence: 79%

Section: Introductionmentioning

confidence: 99%

Proximal-ADMM Decoder for Nonbinary LDPC Codes

Wang,

Bai

2020

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“…where α > 0 is a preset constant. Empirically, the quadratic penalty makes the optimal integer solutions favorable and improves error-correction performance of LDPC decoders significantly [10] [30] [38]. 8 Example: Consider the parity-check equation in F4: c1 + c2 + 2c3 + 3c4 = 0.…”

Section: Proposed Decoding Modelmentioning

confidence: 99%

“…Rosnes in [29] considered adaptive linear programming decoding of linear codes over prime fields and efficient separation of the underlying inequalities describing the decoding polytope which was done through dynamic programming. In addition, Liu et al in [30] and Bai et al in [10] proposed improved ADMM-based penalized decoding algorithms to enhance the error-correction performance of LP decoding in low SNR regions.…”

Section: Introductionmentioning

confidence: 99%

Decoding Nonbinary LDPC Codes via Proximal-ADMM Approach (include convergence proofs)

Wang¹,

Bai²

2022

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In this paper, we focus on decoding nonbinary low-density parity-check (LDPC) codes in Galois fields of characteristic two via the proximal alternating direction method of multipliers (proximal-ADMM). By exploiting Flanagan/Constant-Weighting embedding techniques and the decomposition technique based on three-variables parity-check equations, two efficient proximal-ADMM decoders for nonbinary LDPC codes are proposed. We show that both of them are theoretically guaranteed convergent to some stationary point of the decoding model and either of their computational complexities in each proximal-ADMM iteration scales linearly with LDPC code's length and the size of the considered Galois field. Moreover, the decoder based on the Constant-Weight embedding technique satisfies the favorable property of codeword symmetry. Simulation results demonstrate their effectiveness in comparison with state-of-the-art LDPC decoders.

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“…We note that it is also possible to apply other scheduling schemes [52][53][54][55][56][57][58][59][60][61] proposed for BP decoders on ADMM decoding. As a trade-off between decoding time and memory consumption, the ADMM technique is applied to the LP decomposition model [29] which is equivalent to the original LP decoding model, but with more auxiliary variables, in [62,63]. Other successful simplifications include a software implementation of the ADMM decoding algorithm on a multi-core platform in [64] and a hardware implementation of the ADMM decoding algorithm [65].…”

Section: Complexity Reduction Of Admm Decodingmentioning

confidence: 99%

ADMM Decoding of LDPC Codes: Simplification and Improvement

Wei¹

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In this dissertation, we study linear programming (LP) decoding of low-density parity-check (LDPC) codes based on the alternating direction method of multipliers (ADMM) technique, or ADMM decoding for short. The decoding of LDPC codes is formulated as an LP model and solved efficiently by the ADMM technique. However, compared with traditional belief-propagation decoding, ADMM decoding suffers from higher complexity and worse error correction performance, which prevents the employment of ADMM decoding in reality.To reduce the complexity of ADMM decoding, we first focus on the simplification of the check polytope projection, the most complex operation in ADMM decoding. We propose an iterative check polytope projection algorithm without the sorting operation. The proposed algorithm converges with the increase of iterations. Moreover, for a fixed number of iterations, its average complexity and the worst-case complexity are linear in the input dimension.Another direction we propose to simplify ADMM decoding is to devise a better scheduling scheme than the standard flooding scheme. We start from the node-wise scheduling scheme which only updates the check node messages with the maximum message residual. Then we simplify the calculation of the message residual and propose a reduced-complexity node-wise scheduling scheme.To improve the error correction performance of ADMM decoding, we propose a novel ADMM penalized decoding algorithm whose penalty term is based on check nodes (CN). We investigate the properties of the CN penalty functions and show several examples. We make conclusions on its convergence properties and prove its failure probability is independent of the transmitted codewords for symmetric channels. Monte-Carlo simulation and the instanton analysis show its better error correction performance in the low and high SNR regions.Finally, we propose a post-processing technique to lower the error floor of LDPC codes. The output of the first stage decoder can be revised if the syndrome is found This is a journey with joys and tears. I encountered many amazing people. They instructed me, helped me, and accompanied me.First of all, I would like to thank Prof. Amir H. Banihashemi for his guidance. His attitudes towards the research and devotion to one specific area are impressive. All these will have a life-long influence on me. It is also a great time working with people in his coding research group. I have a great memory of learning from their presentations.Next, I should thank Prof. Xiaopeng Jiao and Prof. Jianjun Mu from Xidian University. They offered me suggestions both in work and life even if we cannot meet with each other as before. More importantly, their encouragement always made me full of confidence in the future.I would like to thank my committee members. Especially, Prof. Ian Marsland kindly reviewed my draft more than once and helped improve the quality of the dissertation significantly. It is a wonderful experience to discuss with him. Prof. Yongyi Mao spared time from his busy schedule for my defen...

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Efficient QP-ADMM Decoder for Binary LDPC Codes and Its Performance Analysis

Cited by 16 publications

References 51 publications

Proximal-ADMM Decoder for Nonbinary LDPC Codes

Proximal-ADMM Decoder for Nonbinary LDPC Codes

Decoding Nonbinary LDPC Codes via Proximal-ADMM Approach (include convergence proofs)

ADMM Decoding of LDPC Codes: Simplification and Improvement

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