A Novel Low-Complexity Joint Coding and Decoding Algorithm for NB-LDPC Codes

Non-binary low-density parity-check (NB-LDPC) codes exhibit a much better performance than their binary counterparts, especially for moderate codeword length and high-order modulation. However, their decoding algorithms suffer from very high computational complexity. In this paper, a low-complexity algorithm is proposed, named parity-check erased algorithm (PCEA), where an additional parity check bit is added to each symbol of the codeword when encoding and a series of simple operations are performed based on these bits during decoding. As a universal joint coding and decoding algorithm, the PCEA can be combined with arbitrary NB-LDPC encoding schemes and decoding algorithms based on message passing. The proposed algorithm facilitates significant improvement of decoding performance with a small decrease of the code rate. Additionally, it usually has an even better performance than a nearly same-rate code constructed by the original method, and requires much lower decoding complexity due to smaller size of the parity check matrix.