Neural-model-augmented hybrid NMS-OSD decoders for near-ML in short block codes

This paper presents a hybrid decoding architecture that serially couples a normalized min-sum (NMS) decoder with reinforced ordered statistics decoding (OSD) to achieve near-maximum likelihood (ML) performance for short linear block codes, including LDPC, BCH, and RS codes. The framework introduces several key innovations. A decoding information aggregation model based on a convolutional neural network refines bit reliability estimates for OSD using the soft-output trajectory of the NMS decoder. An adaptive decoding path for OSD is initialized by the arranged list of the most a priori likely tests algorithm and dynamically updated with empirical data. A sliding-window assisted model enables early termination of test error pattern (TEP) traversal, reducing complexity with minimal performance loss. For short high-rate codes, an undetected error detector identifies erroneous NMS outputs that satisfy parity checks, ensuring they are forwarded to OSD for correction. Extensive simulations on LDPC, BCH, and RS codes demonstrate that the proposed hybrid decoder achieves a competitive trade-off: near-ML frame error rate performance while maintaining advantages in throughput, latency, and complexity over state-of-the-art alternatives. Complexity analysis shows that the average number of OSD TEPs is drastically reduced, and the architecture remains highly parallelizable. An optimization framework is also formulated to balance performance and complexity via parameter tuning.