🤖 AI Summary
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.
📝 Abstract
This paper proposes a quasi-BP decoding scheme for BCH codes that preserves the parallelizable structure of belief propagation while exploiting code automorphisms and optimized redundant parity-check matrices. To eliminate the computationally expensive $\tanh$ and $\tanh^{-1}$ functions in check node updates, we further introduce a neural-network-based variant that replaces them with a lightweight convolutional neural network trained under a triple-constraint loss function enforcing non-negativity and order consistency. Simulation results for three BCH codes demonstrate that quasi-BP decoding achieves competitive frame error rate performance, with a gap within 0.25 decibels compared with belief propagation decoding of an LDPC code of similar blocklength. The neural-network-based variant incurs negligible performance loss while enabling stable deployment with arithmetic operations on hardware accelerators. Concatenation with an ordered statistics decoding variant further bridges the gap to the maximum-likelihood bound. Hence, the proposed schemes offer a viable path toward high-throughput, low-latency decoding of BCH codes in next-generation communication systems.