Reduced Complexity Node-Wise Scheduling of ADMM Decoding for LDPC Codes

Jiao, Xiaopeng; Mu, Jianjun; Wei, Haoyuan

doi:10.1109/lcomm.2016.2643629

Cited by 25 publications

(8 citation statements)

References 17 publications

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“…In these cases, several scheduling algorithms [11]- [13] are proposed, which improve the performance of the standard BP algorithm by updating the outgoing messages of a node (an edge) with an average frequency proportional to the length of local girth and the length of the shortest closed path passing that node (edge). However, to implement these schedules, we found that although the cross-dependency between the incoming messages to a variable node and its initial message is eliminated, the independency between the incoming messages to a variable node and its initial message is also eliminated.…”

Section: Improved Llr-bp Algorithmmentioning

confidence: 99%

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Improved Belief Propagation by Employing the Positive Effects of the Feedback Messages

Cui¹,

Ma²

2019

JCP

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In this paper, a modification to belief propagation (BP) decoding algorithm is proposed, which is based on extracting the prior messages of each variable node to help the BP decoding, and is particularly effective for low-density parity-check (LDPC) codes with short cycles, where the existence of cycles makes the original BP algorithm perform suboptimal. The proposed algorithm, referred to as "employing the positive effects of the feedback messages (EPEFM)", extracts the positive effects of the feedback messages and then makes use of them as prior messages to assist the decoding of the BP algorithm. Simulation results confirm the effectiveness of our proposed algorithm, which improves the performance in high signal-to-noise-ratio (SNR) region without loss in low SNR region.

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Section: Improved Llr-bp Algorithmmentioning

confidence: 99%

“…However, it is still interesting to find a theoretical way to determine appropriate attenuation factors. In [11]- [13], several scheduling algorithms, including probabilistic versus deterministic schedule and node based versus edge based schedule, are presented.…”

Section: Introductionmentioning

confidence: 99%

Improved Belief Propagation by Employing the Positive Effects of the Feedback Messages

Cui¹,

Ma²

2019

JCP

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“…Authors in [36] simplified the check projection operation by jointly using uniform quantization and look-up tables. Moreover, a projection reduction method [37] and two different approaches based on node-wise scheduling and horizontal-layered scheduling in [38] and [39] respectively were proposed to reduce the decoding complexity by decreasing the number of projections. Furthermore, authors in [40] introduced an efficient ADMM-based LP decoding algorithm, which can eliminate the expensive projection operation onto the check polytope.…”

Section: Introductionmentioning

confidence: 99%

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

Bai

Wang

Shi

2020

IEEE Trans. Signal Process.

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This paper presents an efficient quadratic programming (QP) decoder via the alternating direction method of multipliers (ADMM) technique, called QP-ADMM, for binary low-density parity-check (LDPC) codes. Its main contents are as follows: first, we relax maximum likelihood (ML) decoding problem to a non-convex quadratic program. Then, we develop an ADMM solving algorithm for the formulated non-convex QP decoding model. In the proposed QP-ADMM decoder, complex Euclidean projections onto the check polytope are eliminated and variables in each updated step can be solved analytically in parallel. Moreover, it is proved that the proposed ADMM algorithm converges to a stationary point of the non-convex QP problem under the assumption of sequence convergence. We also verify that the proposed decoder satisfies the favorable property of the all-zeros assumption. Furthermore, by exploiting the inside structures of the QP model, the complexity of the proposed algorithm in each iteration is shown to be linear in terms of LDPC code length. Simulation results demonstrate the effectiveness of the proposed QP-ADMM decoder.

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“…In this dissertation, we propose to address the challenges as described in the following. Our main contributions in this dissertation, which are published or submitted for publication in [46], [87], [88], [89], and [90] can be summarized as follows:…”

Section: Summary Of Contributionsmentioning

confidence: 99%

“…• In [87], we apply node-wise scheduling to ADMM decoding and also devise a reduced-complexity node-wise scheduling scheme.…”

Section: Summary Of Contributionsmentioning

confidence: 99%

ADMM Decoding of LDPC Codes: Simplification and Improvement

Wei¹

Self Cite

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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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Reduced Complexity Node-Wise Scheduling of ADMM Decoding for LDPC Codes

Cited by 25 publications

References 17 publications

Improved Belief Propagation by Employing the Positive Effects of the Feedback Messages

Improved Belief Propagation by Employing the Positive Effects of the Feedback Messages

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

ADMM Decoding of LDPC Codes: Simplification and Improvement

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