Hybrid Decoding of BP and ADMM for LDPC Codes

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.