Quasi-Belief Propagation and Neural-Network Check Node Processing for BCH Codes
This work addresses the high decoding complexity and suboptimal performance of conventional belief propagation (BP) decoding for BCH codes compared to LDPC codes. The authors propose a quasi-BP decoding framework that integrates code automorphism structures with an optimized redundant parity-check matrix and, for the first time, embeds a lightweight convolutional neural network into check nodes to replace the computationally intensive tanh and inverse-tanh operations. A triple-constraint loss function is designed to enforce non-negativity and order consistency in the outputs, enabling seamless concatenation with ordered statistics decoding. Experiments on three BCH codes demonstrate that the proposed method achieves performance within approximately 0.25 dB of the maximum-likelihood bound—comparable to LDPC codes of similar blocklength—while the neural-network-based variant incurs negligible performance loss, supporting efficient hardware implementation.