A BRB Algorithm for Non-Binary LDPC Decoding With Single-Symbol Extrinsic Information Modification

Abstract

In the weighted bit-reliability based (wBRB) Non-binary LDPC decoding algorithm, using the minimum bit-reliability as the reliability of the entire symbol for information updating significantly decreases the decoding performance in cases of a large order of Galois field or small column weight. The improved algorithm——MwBRB increases the decoding performance by introducing three kinds of extrinsic information transfer but suffers from high decoding complexity. To address these problems, a BRB Non-binary LDPC decoding algorithm based on single-symbol extrinsic information modification is proposed. At the variable node $V_{j}$ , using a symbol-related reliability calculation method, the maximum reliability information and its corresponding most possible Galois field symbol are obtained, and then transferred to the check node $C_{i}$ ; at the check node $C_{i}$ , only the most possible Galois field symbol is used for extrinsic information processing, and its reliability of the extrinsic information is represented by the minimum reliability of other Galois field symbols. Finally, at the check node $C_{i}$ , the extrinsic information is processed by based on the Hamming distance coefficient in terms of bits. Simulation and performance analysis show that the proposed algorithm reduces the complexity by over 50% compared to the MwBRB algorithm, and maintains consistent or slightly superior decoding performance. Additionally, the proposed algorithm exhibits similar decoding performance to LDPC codes constructed by different methods and shows better robustness.

Keywords

• Non-binary LDPC codes
• single-symbol
• extrinsic information
• reliability-based decoding
• hamming distance