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arXiv:2605.10681

Scalable Mamba-Based Message-Passing Neural Decoder for Error-Correcting Codes

Rostislav Gusev, Nikita Aleksandrov, Artem Solomkin, Dmitry Artemasov

Published May 11, 2026• 0 citations
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Abstract

Forward error correction is essential for reliable communication over noisy channels. Attention-based model-free neural decoders have shown strong performance for short codes, but their scalability to longer codes is limited by the quadratic memory and computational cost of attention. In this paper, we introduce the Mamba message-passing decoder (MMPD), an attention-free syndrome-based neural decoder for binary linear codes. MMPD retains the Tanner-graph structure of a message-passing decoder by performing local pairwise aggregation along variable-check edges. To enable efficient long-range information propagation, these local updates are combined with bidirectional Mamba state-space blocks. By avoiding dense attention matrices, MMPD scales more favorably for long codes in both memory and computation. Experiments on the (1056, 880) LDPC code show that MMPD achieves a 0.45 dB gain over the state-of-the-art CrossMPT decoder at a specified target bit error rate, while reducing memory consumption by a factor of 1.5. This reduction factor increases substantially for longer codes, demonstrating the applicability of MMPD to scalable neural decoding of practical long codes.

DOI
10.48550/arxiv.2605.10681

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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.
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Transformer-based neural decoders have emerged as a promising approach to error correction coding, combining data-driven adaptability with efficient modeling of long-range dependencies. This paper presents a novel decoder architecture that integrates classical belief propagation principles with transformer designs. We introduce a differentiable syndrome loss function leveraging global codebook structure and a differential-attention mechanism optimizing bit and syndrome embedding interactions. Experimental results demonstrate consistent performance improvements over existing transformer-based decoders, with our approach surpassing traditional belief propagation decoders for short-to-medium length LDPC codes.
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In this work, we propose a novel decoding algorithm for short block codes based on an edge-weighted graph neural network (EW-GNN). The EW-GNN decoder operates on the Tanner graph with an iterative message-passing structure, which algorithmically aligns with the conventional belief propagation (BP) decoding method. In each iteration, the “weight” on the message passed along each edge is obtained from a fully connected neural network that has the reliability information from nodes/edges as its input. Compared to existing deep-learning-based decoding schemes, the EW-GNN decoder is characterised by its scalability, meaning that 1) the number of trainable parameters is independent of the codeword length, and 2) an EW-GNN decoder trained with shorter/simple codes can be directly used for longer/sophisticated codes of different code rates. Furthermore, simulation results show that the EW-GNN decoder outperforms the BP and deep-learning-based BP methods from the literature in terms of the decoding error rate.