CrossMPM: Cross-Selective Scan Message-Passing Mamba for Short-Length LDPC Codes

Error-correcting codes (ECCs) are fundamental to reliable communication over noisy channels. Transformer-based neural decoders achieve strong ECC decoding performance, but attention operations cause computational complexity to grow substantially with code length. We propose Cross-Selective Scan Message-Passing Mamba (CrossMPM), a low-complexity Mamba-based neural decoder, to address this issue. CrossMPM replaces cross-attention-based information exchange between magnitude and syndrome vectors in Cross-Attention Message-Passing Transformer (CrossMPT) with Tanner-graph projection and Cross-Selective Scan State-Space Model (Cross-Selective Scan SSM). Tanner-graph projection aggregates connected node representations according to the parity-check matrix to incorporate code structure, while Cross-Selective Scan SSM dynamically generates selection parameters from the aggregated representations to control state updates and outputs. CrossMPM thus models local parity constraints and long-range dependencies without attention operations and reduces computational complexity. Simulation results show that CrossMPM achieves competitive decoding performance with lower computational complexity than CrossMPT and Hybrid Mamba-Transformer Decoder (ECCM), and this performance is maintained at longer code lengths. These results show that CrossMPM provides a favorable trade-off between error correction performance and computational efficiency.