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IEEE Communications Letters

Fast Converging ADMM-Penalized Algorithm for LDPC Decoding

Imen Debbabi, Bertrand Le Gal, Nadia Khouja, Fethi Tlili, Christophe Jégo

Published Feb 19, 2016• 39 citations
Publisher

Abstract

The alternate direction method of multipliers (ADMM) approach has been recently considered for LDPC decoding. It has been approved to enhance the error rate performance compared with conventional message passing (MP) techniques in both the waterfall and error floor regions at the cost of a higher computation complexity. In this letter, a formulation of the ADMM decoding algorithm with modified computation scheduling is proposed. It increases the error correction performance of the decoding algorithm and reduces the average computation complexity of the decoding process thanks to a faster convergence. Simulation results show that this modified scheduling speeds up the decoding procedure with regards to the ADMM initial formulation while enhancing the error correction performance. This decoding speed-up is further improved when the proposed scheduling is teamed with a recent complexity reduction method detailed in Wei et al.IEEE Commun. Lett., 2015.

DOI
10.1109/lcomm.2016.2531040

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The alternate direction method of multipliers (ADMM) approach has been recently considered for LDPC decoding. It has been approved to enhance the error rate performance compared with conventional message passing (MP) techniques in both the waterfall and error floor regions at the cost of a higher computation complexity. In this letter, a formulation of the ADMM decoding algorithm with modified computation scheduling is proposed. It increases the error correction performance of the decoding algorithm and reduces the average computation complexity of the decoding process thanks to a faster convergence. Simulation results show that this modified scheduling speeds up the decoding procedure with regards to the ADMM initial formulation while enhancing the error correction performance. This decoding speed-up is further improved when the proposed scheduling is teamed with a recent complexity reduction method detailed in Wei et al.IEEE Commun. Lett., 2015.
For low-density parity-check (LDPC) codes, the penalized decoding method based on the alternating direction method of multipliers (ADMM) can improve the decoding performance at low signal-to-noise ratios and also has low decoding complexity. There are three effective methods that could increase the ADMM penalized decoding speed, which are reducing the number of Euclidean projections in ADMM penalized decoding, designing an effective penalty function and selecting an appropriate layered scheduling strategy for message transmission. In order to further increase the ADMM penalized decoding speed, through reducing the number of Euclidean projections and using the vertical layered scheduling strategy, this paper designs a fast converging ADMM penalized decoding method based on the improved penalty function. Simulation results show that the proposed method not only improves the decoding performance but also reduces the average number of iterations and the average decoding time.
The alternating direction method of multipliers (ADMM) approach to decoding low-density parity-check (LDPC) codes has garnered lots of attention due to its superior error correction performance in error floor regions. However, improving convergence characteristic of ADMM decoding efficiently remains to be a crucial but challenging issue for practical application. In order to tackle this challenge, in this paper we first propose an efficient Pro-ADMM-based decoding algorithm framework by inserting additional quadratic proximal terms to each iteration of ADMM decoding for stabilizing the variable updates. Second, an message-passing interpretation of Pro-ADMM decoder is considered, and then an improved version based on horizontal layered scheduling, named Pro-ADMM-HL decoder is developed to further enhance the convergence behavior of Pro-ADMM decoding. Additionally, we analyze that the complexity of the proposed Pro-ADMM-HL decoders at each iteration displays linearly to LDPC code length. Finally, the effectiveness of the proposed Pro-ADMM and Pro-ADMM-HL decoding algorithm in terms of error correction performance and convergence characteristic is demonstrated by simulation results.
A node-wise (NS) schedule has been recently proposed for decoding LDPC codes with the linear programming (LP) decoding approach, based on the alternate direction method of multipliers (ADMM). It improves the error correction performances as well as the convergence speed of the ADMM-LP decoder. However, it suffers from a high computational complexity resulted from residuals calculation. In this paper, a new formulation of the ADMM-LP algorithm with a modified computational scheduling is proposed for decoding LDPC convolutional codes. Simulations show that it reduces the computational complexity while improving the error correction performances and speeding up the decoding process. The decoding complexity is further reduced when considering the NS-ADMM approximation which allows savings up to 70% of the residuals calculation.
Alternate direction method of multipliers (ADMM) technique has recently been proposed for LDPC decoding. Even though it improves the error rate performance compared with traditional message passing (MP) techniques, it shows a higher computation complexity. In this article, the ADMM decoding algorithm is first described. Then, its computation complexity is analyzed. Finally, an optimized version which benefits from the multi-core processors architecture as well as the ADMM algorithm s parallelism is presented. The optimized version of the ADMM decoder can achieve up to 30 Mbps for standardized LDPC codes on a laptop x86 processor. Therefore, it could guide an efficient GPU implementation for real-time and high-throughput decoding systems requiring correction performances beyond MP-Sum Product Algorithm (SPA) capabilities.
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.
LDPC decoding algorithm based on the alternating direction method of multipliers (ADMM) technique has increased much attentions because of its outstanding decoding performance. To enhancing performance advantages of ADMM decoding in practical application, a main challenge is to design an efficient penalty function and then customize an accelerating decoding algorithm. To address this issue, in this paper we propose an improved penalized decoding problem based on a segmented penalty function (SPF), and then develop an efficient ADMM algorithm via optimizing variable updating to solve this SPF-based decoding model. Experimental simulations demonstrate that the proposed algorithm effectively reduces the number of iterations while achieving better error-correction performance, when compared to the state-of-the-art ADMM-based decoding algorithms.