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.
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.
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.
In this paper, we propose a novel deep learning-based framework for the joint design and decoding of linear block codes, the end-to-end deep coding cross-attention message-passing Transformer (E2E DC-CrossMPT). To improve linear block code design and decoding, we redesign the conventional error correction code (ECC) decoder, CrossMPT, to fit within an end-to-end framework. The redesigned decoder separately utilizes magnitude and syndrome vectors obtained from the received signals as inputs. It further employs one-hot encoding based syndrome embedding and incorporates a parity-check matrix into the output layers. Experimental results demonstrate that, across various code lengths and code rates, E2E DC-CrossMPT consistently outperforms both traditional decoding algorithms and a conventional end-to-end deep coding model in terms of decoding performance. Moreover, the codes designed by E2E DC-CrossMPT achieve superior error-correction capability compared with both traditional linear block codes and those designed by the conventional end-to-end deep coding model, while requiring lower computational complexity.
Recently, deep learning has demonstrated improvements over classical decoding algorithms in various families of error-correcting codes with short to moderate block lengths. Neural decoders like neural belief propagation (NBP), constructed based on the Tanner graphs of linear codes, have been extensively studied, but their application to longer codes is limited due to increased network complexity with longer block lengths. This complexity leads to higher computational costs and deployment challenges, such as GPU memory usage. To address this, we propose a novel revolving framework for NBP-like decoders tailored to cyclic and QC-LDPC codes, a commonly used class of error correction codes. Our approach leverages the cyclic structure and section-wise cyclic structure inherent in cyclic and QC-LDPC codes respectively, significantly simplifying the complexity of the network. Experimental results demonstrate the effectiveness of our method across various cyclic and QC-LDPC codes. Especially, compared to the traditional decoding scheme based on the section-wise cyclic structure, our proposed decoder shows substantial improvements on 5G LDPC codes, exhibits better performance than the traditional min-sum decoder, and approaches the sum-product decoder without a noticeable error floor within the investigated noise levels.
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.
Recently, deep learning has demonstrated improvements over classical decoding algorithms in various families of error-correcting codes with short to moderate block lengths. Neural decoders like neural belief propagation (NBP), constructed based on the Tanner graphs of linear codes, have been extensively studied, but their application to longer codes is limited due to increased network complexity with longer block lengths. This complexity leads to higher computational costs and deployment challenges, such as GPU memory usage. To address this, we propose a novel revolving framework for NBP-like decoders tailored to QC-LDPC codes, a commonly used class of error correction codes. Our approach leverages the section-wise cyclic structure inherent in QC-LDPC codes, significantly simplifying the complexity of the network. Experimental results demonstrate the effectiveness of our method across various QC-LDPC codes. Especially, compared to the traditional decoding scheme based on the section-wise cyclic structure, our proposed decoder shows substantial improvements on 5G LDPC codes, exhibits better performance than the traditional min-sum decoder, and approaches the sum-product decoder without a noticeable error floor within the investigated noise levels.
Error correction code is a major part of the communication physical layer, ensuring the reliable transfer of data over noisy channels. Recently, neural decoders were shown to outperform classical decoding techniques. However, the existing neural approaches present strong overfitting due to the exponential training complexity, or a restrictive inductive bias due to reliance on Belief Propagation. Recently, Transformers have become methods of choice in many applications thanks to their ability to represent complex interactions between elements. In this work, we propose to extend for the first time the Transformer architecture to the soft decoding of linear codes at arbitrary block lengths. We encode each channel's output dimension to high dimension for better representation of the bits information to be processed separately. The element-wise processing allows the analysis of the channel output reliability, while the algebraic code and the interaction between the bits are inserted into the model via an adapted masked self-attention module. The proposed approach demonstrates the extreme power and flexibility of Transformers and outperforms existing state-of-the-art neural decoders by large margins at a fraction of their time complexity.