🤖 AI Summary
BCH short-code decoding suffers from high undetected error rates, slow iterative convergence, and rigid algebraic structure limiting performance. Method: This paper proposes a low-complexity, high-robustness belief propagation (BP) decoding framework. Its core innovations are: (1) a heuristic sparsification method—binary summation combined with cyclic shifts—to construct a low-density, quasi-regular parity-check matrix with few short cycles; and the first systematic quantification of the relationship among frame error rate, dual-code minimum-weight codeword rank deficiency, and row redundancy; (2) integration of three types of random automorphism injections and iterative message aggregation to enhance error-pattern diversity and suppress undetected errors. Results: At comparable throughput, the proposed decoder achieves 1–2 dB BER gain over parallel algebraic decoders, reduces average iteration count by two orders of magnitude, and significantly improves decoding reliability and real-time performance for short BCH codes.
📝 Abstract
High-throughput decoding of BCH codes necessitates efficient and parallelizable decoders. However, the algebraic rigidity of BCH codes poses significant challenges to applying parallel belief propagation variants. To address this, we propose a systematic design scheme for constructing parity-check matrices using a heuristic approach. This involves a sequence of binary sum operations and row cyclic shifts on the standard parity-check matrix, aiming to generate a redundant, low-density, and quasi-regular matrix with significantly fewer length-4 cycles. The relationships between frame error rate, rank deficiency of minimum-weight dual-code codewords, and row redundancy are empirically analyzed. For the revised normalized min-sum decoder, we introduce three types of random automorphisms applied to decoder inputs. These are unpacked and aggregated by summing messages after each iteration, achieving a 1-2dB improvement in bit error rate compared to parallelizable counterparts and two orders of magnitude faster convergence in iterations than iterative rivals. Additionally, undetected errors are highlighted as a non-negligible issue for very short BCH codes.