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arXiv:2405.01033

CrossMPT: Cross-attention Message-Passing Transformer for Error Correcting Codes

Seong‐Joon Park, Kwak, Hee-Youl, Sang‐Hyo Kim, Yongjune Kim, Jong‐Seon No

Published May 2, 2024• 1 citation
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Abstract

Error correcting codes (ECCs) are indispensable for reliable transmission in communication systems. The recent advancements in deep learning have catalyzed the exploration of ECC decoders based on neural networks. Among these, transformer-based neural decoders have achieved state-of-the-art decoding performance. In this paper, we propose a novel Cross-attention Message-Passing Transformer (CrossMPT), which shares key operational principles with conventional message-passing decoders. While conventional transformer-based decoders employ self-attention mechanism without distinguishing between the types of input vectors (i.e., magnitude and syndrome vectors), CrossMPT updates the two types of input vectors separately and iteratively using two masked cross-attention blocks. The mask matrices are determined by the code's parity-check matrix, which explicitly captures the irrelevant relationship between two input vectors. Our experimental results show that CrossMPT significantly outperforms existing neural network-based decoders for various code classes. Notably, CrossMPT achieves this decoding performance improvement, while significantly reducing the memory usage, complexity, inference time, and training time.

DOI
10.48550/arxiv.2405.01033

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Error correcting codes (ECCs) are indispensable for reliable transmission in communication systems. The recent advancements in deep learning have catalyzed the exploration of ECC decoders based on neural networks. Among these, transformer-based neural decoders have achieved state-of-the-art decoding performance. In this paper, we propose a novel Cross-attention Message-Passing Transformer (CrossMPT), which shares key operational principles with conventional message-passing decoders. While conventional transformer-based decoders employ self-attention mechanism without distinguishing between the types of input vectors (i.e., magnitude and syndrome vectors), CrossMPT updates the two types of input vectors separately and iteratively using two masked cross-attention blocks. The mask matrices are determined by the code's parity-check matrix, which explicitly captures the irrelevant relationship between two input vectors. Our experimental results show that CrossMPT significantly outperforms existing neural network-based decoders for various code classes. Notably, CrossMPT achieves this decoding performance improvement, while significantly reducing the memory usage, complexity, inference time, and training time.
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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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In communication and storage systems, error correction codes (ECCs) are pivotal in ensuring data reliability. As deep learning's applicability has broadened across diverse domains, there is a growing research focus on neural network-based decoders that outperform traditional decoding algorithms. Among these neural decoders, Error Correction Code Transformer (ECCT) has achieved the state-of-the-art performance, outperforming other methods by large margins. To further enhance the performance of ECCT, we propose two novel methods. First, leveraging the systematic encoding technique of ECCs, we introduce a new masking matrix for ECCT, aiming to improve the performance and reduce the computational complexity. Second, we propose a novel transformer architecture of ECCT called a double-masked ECCT. This architecture employs two different mask matrices in a parallel manner to learn more diverse features of the relationship between codeword bits in the masked self-attention blocks. Extensive simulation results show that the proposed double-masked ECCT outperforms the conventional ECCT, achieving the state-of-the-art decoding performance with significant margins.
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