Reduced-Complexity Belief Propagation Decoding for LDPC Codes

Heping Wan

doi:10.1109/ACCESS.2026.3673136

Reduced-Complexity Belief Propagation Decoding for LDPC Codes

2026-01-01

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Charlie Jianzhong Zhang

DOI：10.1109/ACCESS.2026.3673136

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Two methods are proposed to reduce the complexity of the belief propagation (BP) decoding for low-density parity-check (LDPC) codes, with the focus on the layered decoding for quasi-cyclic LDPC (QC-LDPC) codes. The two methods can be separately incorporated into the layered decoding procedures and combined seamlessly to provide the two-fold complexity reduction. In the first method, the message updates regarding a subset of variable nodes are omitted. To construct the subset, the most reliable bit-level channels, derived from $M$ -ary input channels, are identified. Then, we select the variable nodes with initial log-likelihood ratios (LLRs) exceeding a threshold among the ones assigned to the most reliable bit-level channels to form the subset. The threshold is designed and adjusted based on characteristics of the most reliable bit-level channels. Our numerical results demonstrate that the first method significantly reduces the complexity with negligibly impacting the error-correcting performance. In the second method, each layer of base graphs of QC-LDPC codes uses either sum-product algorithm (SPA) or min-sum algorithm (MSA) to update LLRs. A degree-based algorithm is presented to determine the layers employing either SPA or MSA. We compare with two intuitive methods: 1) applying SPA to randomly selected layers and MSA to the remaining layers, and 2) applying SPA to the core layers of 5G NR LDPC codes and MSA to the remaining layers. According to the numerical results, the degree-based algorithm maximally reduces the complexity while maintaining the same performance. To evaluate the joint method, the first method is applied on top of the second method. Further complexity reduction is achieved without degrading the performance of the second method.

Keywords:

Iterative decoding

Decoding

Complexity theory

Reliability

5G mobile communication

Schedules

Parallel processing

Convergence

Systematics

Symbols

LDPC codes

belief propagation decoding

reduced complexity

Reduced-Complexity Belief Propagation Decoding for LDPC Codes

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