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IEEE Communications Letters

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

Xiaopeng Jiao, Jianjun Mu, Haoyuan Wei

Published Dec 22, 2016• 25 citations
Publisher

Abstract

Similar to the belief propagation decoder, linear programming decoding based on the alternating direction method of multipliers (ADMM) can also be seen as an iterative message-passing decoding algorithm. How to schedule messages efficiently is an important aspect since it will influence the convergence rate of iterative decoders. In this letter, we investigate the node-wise scheduling for ADMM decoders, named NS-ADMM. In particular, we propose a reduced-complexity method for the NS-ADMM decoder by avoiding Euclidean projections involved in the calculation of message residuals. Simulation results show that the proposed method converges much faster than the flooding and layered scheduling while keeping a lower complexity when compared with the NS-ADMM decoder.

DOI
10.1109/lcomm.2016.2643629

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Similar to the belief propagation decoder, linear programming decoding based on the alternating direction method of multipliers (ADMM) can also be seen as an iterative message-passing decoding algorithm. How to schedule messages efficiently is an important aspect since it will influence the convergence rate of iterative decoders. In this letter, we investigate the node-wise scheduling for ADMM decoders, named NS-ADMM. In particular, we propose a reduced-complexity method for the NS-ADMM decoder by avoiding Euclidean projections involved in the calculation of message residuals. Simulation results show that the proposed method converges much faster than the flooding and layered scheduling while keeping a lower complexity when compared with the NS-ADMM decoder.
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.
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.
The Euclidean projection onto check polytopes is the most time-consuming operation in the linear programming (LP) decoding based on alternating direction method of multipliers (ADMM) for low-density parity-check (LDPC) codes. In this letter, instead of reducing the complexity of Euclidean projection itself, we propose a new method to reduce the decoding complexity of ADMM-based LP decoder by decreasing the number of Euclidean projections. In particular, if all absolute values of the element-wise differences between the input vector of Euclidean projection in the current iteration and that in the previous iteration are less than a predefined value, then the Euclidean projection at the current iteration will be no longer performed. Simulation results show that the proposed decoder can still save roughly 20% decoding time even if both the over-relaxation and early termination techniques are used.
In order to simplify the node-wise scheduling algorithm of the alternating direction method of multipliers (NS-ADMM) decoding, approximate line segment projection algorithm (LSA) is adopted to perform the projection in the node-wise scheduling algorithm. Experimental results show that using approximate line segment projection instead of precise projection in node-wise scheduling algorithm will yield a poor frame error rate (FER) performance. To solve this problem, dynamic scheduling strategy that selects the message-passing schedule according to the convergence status of the check node is proposed. Simulation results demonstrate that the modified node-wise scheduling algorithm based on line segment projection outperforms existing decoding algorithms in terms of FER performance and convergence speed, while it has good error correction performance with a lower computational complexity.
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.
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.