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IEEE International Conference on Communication Technology (ICCT)

Hybrid Decoding of BP and ADMM for LDPC Codes

Dong Wang, Zhiping Shi, Li Juan DENG

Published Nov 11, 2022• 0 citations
Publisher

Abstract

The alternating direction method of multipliers (ADMM) algorithm has been used in the linear programming decoding of low-density parity-check (LDPC) codes in recent years. The ADMM has similar complexity with the belief propagation (BP) algorithm and better performance under some conditions. In this paper, we propose a hybrid decoder based on BP and ADMM-penalized decoder, which is called BP-ADMM decoder. In order to reduce the undetectable error of probability (UEP) after BP decoding as much as possible, we add cyclic redundancy check (CRC) before LDPC encoding. Before the output of the hybrid decoder, we add a Hamming distance comparison decision, and select the codeword with a smaller Hamming distance from the initial hard decision as the output.

DOI
10.1109/icct56141.2022.10073262

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The alternating direction method of multipliers (ADMM) algorithm has been used in the linear programming decoding of low-density parity-check (LDPC) codes in recent years. The ADMM has similar complexity with the belief propagation (BP) algorithm and better performance under some conditions. In this paper, we propose a hybrid decoder based on BP and ADMM-penalized decoder, which is called BP-ADMM decoder. In order to reduce the undetectable error of probability (UEP) after BP decoding as much as possible, we add cyclic redundancy check (CRC) before LDPC encoding. Before the output of the hybrid decoder, we add a Hamming distance comparison decision, and select the codeword with a smaller Hamming distance from the initial hard decision as the output.
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.
Decoding by alternating direction method of multipliers (ADMM) is a promising linear programming decoder for low-density parity-check (LDPC) codes. In this paper, we propose a two-step scheme to lower the error floor of LDPC codes with ADMM penalized decoder. For the undetected errors that cannot be avoided at the decoder side, we modify the code structure slightly to eliminate low-weight code words. For the detected errors induced by small error-prone structures, we propose a post-processing method for the ADMM penalized decoder. Simulation results show that the error floor can be reduced significantly over three illustrated LDPC codes by the proposed two-step scheme.
In this paper, we present a new class of decoders for low density parity check (LDPC) codes. We are motivated by the observation that the linear programming (LP) decoder has worse error performance than belief propagation (BP) decoders at low SNRs. We base our new decoders on the alternating direction method of multipliers (ADMM) decomposition technique for LP decoding. The ADMM not only efficiently solves the LP decoding problem, but also makes it possible to explore other decoding algorithms. In particular, we add various penalty terms to the linear objective of LP decoding with the goal of suppressing pseudocodewords. Simulation results show that the new decoders achieve much better error performance compared to LP decoder at low SNRs. What is more, similar to the LP decoder, no error floor is observed at high SNRs.
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 Alternating Direction Method of Multipliers (ADMM) has proven to be an efficient approach for implementing linear programming (LP) decoding of low-density parity-check (LDPC) codes. By introducing penalty terms into the LP decoding model's objective function, ADMM-based variable node penalized decoding effectively mitigates non-integral solutions, thereby improving frame error rate (FER) performance, especially in the low signal-to-noise ratio (SNR) region. In this paper, we leverage the ADMM framework to derive explicit iterative steps for solving the LP decoding problem for LDPC codes with penalty functions. To further enhance decoding efficiency and accuracy, We propose an LDPC code decoding algorithm based on the symmetric ADMM (S-ADMM). We also establish some contraction properties satisfied by the iterative sequence of the algorithm. Through simulation experiments, we evaluate the proposed S-ADMM decoder using three standard LDPC codes and three representative fifth-generation (5G) codes. The results show that the S-ADMM decoder consistently outperforms conventional ADMM penalized decoders, offering significant improvements in decoding performance.
Alternating direction method of multipliers (ADMM) is an efficient implementation of linear programming (LP) decoding for low-density parity-check (LDPC) codes. By adding penalty terms to the objective function of the LP decoding model, ADMM variable node (VN) penalized decoding can suppress the non-integral solutions and improve the frame error rate (FER) performance in the low signal-to-noise ratio (SNR) region. In this paper, we propose a novel ADMM check node (CN) penalized decoding algorithm. Codeword solutions which satisfy all parity-check equations will have smaller penalty values than non-codeword solutions, including the non-integral solutions. We discuss the required properties of CN-penalty functions, propose a few functions that satisfy those properties, and study their performance/complexity trade-offs. We also investigate the convergence properties of the proposed algorithm and prove that its performance is independent of the transmitted codeword. Using Monte Carlo simulations and instanton analysis, we then demonstrate that the proposed CN-penalized decoder outperforms ADMM VN penalized decoders in both waterfall and error floor regions. This comes at the expense of some increase in the decoding complexity.