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IEEE Access

Horizontal Layered Scheduling ADMM Penalized Decoder Based on the Improved Penalty Function for LDPC

Biao Wang, Zhongfei Wang

Published Jan 1, 2022• 1 citation
Publisher

Abstract

For low-density parity-check (LDPC) codes, reducing the number of Euclidean projections, choosing a suitable scheduling strategy, and devising an improved penalty function are three effective ways to increase the alternating direction method of multipliers (ADMM) penalized decoding speed. By combining the above three ways, this paper proposes a horizontal layered scheduling ADMM penalized decoder based on the improved penalty function to speed up decoding. The experimental data indicate that the proposed decoder can obtain better performance and lower average number of iterations than the existing ADMM penalized decoders.

DOI
10.1109/access.2022.3224226

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For low-density parity-check (LDPC) codes, reducing the number of Euclidean projections, choosing a suitable scheduling strategy, and devising an improved penalty function are three effective ways to increase the alternating direction method of multipliers (ADMM) penalized decoding speed. By combining the above three ways, this paper proposes a horizontal layered scheduling ADMM penalized decoder based on the improved penalty function to speed up decoding. The experimental data indicate that the proposed decoder can obtain better performance and lower average number of iterations than the existing ADMM penalized decoders.
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.
By making the pseudocodewords more costly than codewords, the alternating direction method of multipliers (ADMM) penalized decoder can improve the error rate performances significantly for low-density parity-check (LDPC) codes at low signal-to-noise ratios. In this letter, we design two improved piecewise penalty functions for ADMM penalized decoder by increasing the slope of the penalty function at the points near x = 0 and x = 1. The improved penalty functions can punish pseudocodewords more quickly and thus increase the decoding speed. Simulation results over two LDPC codes show that the proposed method improves the error rate performances and reduces the decoding time considerably.
Based on linear programming (LP) decoding with alternating direction method of multipliers (ADMM), Liu et al. proposed an ADMM penalized decoder for low-density parity-check (LDPC) codes that can improve the error rate performance at low signal-to-noise ratios. In this letter, we propose a new ADMM penalized decoder to improve the error rate performance further for irregular LDPC codes. The proposed decoder modifies the penalty term of the objective function by assigning different penalty parameters for different variable node degrees. Simulations over three irregular LDPC codes show that the proposed decoder performs considerably better than the ADMM penalized decoder.
The Euclidean projection onto check polytope is the most complicated and time-consuming operation in the alternating direction method of multipliers (ADMM) decoding for Low-Density Parity-Check (LDPC) codes. The check polytope projection penalized algorithm can avoid the tedious work of penalty parameter optimization and simplified the calculation process of check polytope projection. However, the over-punishment of check polytope projection penalized algorithm may lead to poor decoding performance, when combined with the over-relaxation technique. In this paper, an improved check polytope projection penalized algorithm is proposed. In order to reduce the ratio of even-vertex projection, we restrict the points far away from the even-vertex of the check polytope by introducing the penalty constraint condition. Simulation results show that the frame error rate (FER) performance of the proposed algorithm is almost the same as that of the cut search projection algorithm (CSA), and it can save the average decoding time by 22.9%–52%.
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.
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.