Improved Penalty Functions of ADMM Penalized Decoder for LDPC Codes

Wang, Biao; Mu, Jianjun; Jiao, Xiaopeng; Wang, Zhongfei

doi:10.1109/lcomm.2016.2627575

Cited by 20 publications

(15 citation statements)

References 8 publications

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“…In [17], Wei et al reduce the runtime by avoiding projections whenever the change in the input of the projection is sufficiently small. New piecewise penalty terms are introduced by Wang et al in [18]. In [19], Jiao et al compare two improving techniques of ADMM in the context of LP decoding, namely over-relaxation [4] and accelerated ADMM [20].…”

Section: Related Workmentioning

confidence: 99%

A Low-Complexity Projection Algorithm for ADMM-Based LP Decoding

Gensheimer

Dietz

Ruzika

et al. 2018

2018 IEEE 10th International Symposium on Turbo Codes &Amp; Iterative Information Processing (ISTC)

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The Alternating Direction Method of Multipliers has recently been adapted for Linear Programming Decoding of Low-Density Parity-Check codes. The computation of the projection onto the parity polytope is the core of this algorithm and usually involves a sorting operation, which is the main effort of the projection.In this paper, we present an algorithm with low complexity to compute this projection. The algorithm relies on new findings in the recursive structure of the parity polytope and iteratively fixes selected components. It requires up to 37% less arithmetical operations compared to state-of-the-art projections. Additionally, it does not involve a sorting operation, which is needed in all exact state-of-the-art projection algorithms. These two benefits make it appealing for efficient hard-and software implementations.

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Section: Related Workmentioning

confidence: 99%

A Low-Complexity Projection Algorithm for ADMM-Based LP Decoding

Gensheimer

Dietz

Ruzika

et al. 2018

2018 IEEE 10th International Symposium on Turbo Codes &Amp; Iterative Information Processing (ISTC)

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“…The authors in [6] improved the error-correcting performance through an ADMM-penalized decoder, where the idea is to make pseudocodewords more costly by adding various penalty terms to the objective function. Moreover, in [7], the ADMMpenalized decoder was further improved by using piecewise penalty functions, and for irregular LDPC codes, the work [8] proposed to modify the penalty term and assign different penalty parameters for variable nodes with different degrees.…”

Section: Introductionmentioning

confidence: 99%

ADMM-Based Decoder for Binary Linear Codes Aided by Deep Learning

2020

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Inspired by the recent advances in deep learning (DL), this work presents a deep neural network aided decoding algorithm for binary linear codes. Based on the concept of deep unfolding, we design a decoding network by unfolding the alternating direction method of multipliers (ADMM)-penalized decoder. In addition, we propose two improved versions of the proposed network. The first one transforms the penalty parameter into a set of iteration-dependent ones, and the second one adopts a specially designed penalty function, which is based on a piecewise linear function with adjustable slopes. Numerical results show that the resulting DL-aided decoders outperform the original ADMM-penalized decoder for various low density parity check (LDPC) codes with similar computational complexity.

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“…They efficiently optimized the multiple penalty coefficients by differential evolution, and the frame error rate (FER) performance of the decoder is further improved. In [68], Wang et al used a segmented function as the penalty term and optimized the relevant parameters by differential evolution. The convergence speed and the FER performance are shown to be improved.…”

Section: Performance Improvement Of Admm Decodingmentioning

confidence: 99%

“…The factional points are called pseudo-codewords and degrade the error correction performance. To penalize pseudo-codewords, ADMM VN-penalized decoding algorithms [66][67][68] were proposed by adding penalty terms to the objective function of the LP decoding model. For example, ADMM VN-penalized decoding algorithm with 2 penalty terms, h 2 (x) = −α(x − 0.5) 2 , significantly improved the FER performance in the low SNR region with only the updating rule variable x i changed as follows:…”

Section: Admm Decoding Modelmentioning

confidence: 99%

“…In order to improve the error correction performance of ADMM decoding at low SNR values, penalty terms were added to the objective function of the LP decoding model to penalize the pseudo-codewords. All previous ADMM penalized decoding algorithms [66][67][68] penalize the invalid solutions from the aspect of the variable nodes and are referred to ADMM VN-penalized decoders.…”

Section: Admm Cn-penalized Decodermentioning

confidence: 99%

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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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Improved Penalty Functions of ADMM Penalized Decoder for LDPC Codes

Cited by 20 publications

References 8 publications

A Low-Complexity Projection Algorithm for ADMM-Based LP Decoding

A Low-Complexity Projection Algorithm for ADMM-Based LP Decoding

ADMM-Based Decoder for Binary Linear Codes Aided by Deep Learning

ADMM Decoding of LDPC Codes: Simplification and Improvement

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