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.
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.
With the broadening applications of deep learning, neural decoders have emerged as a key research focus, specifically aimed at improving the decoding performance of conventional decoding algorithms. In particular, error correction code transformer (ECCT), which utilizes the transformer architecture, has achieved state-of-the-art performance among neural network-based decoders. We present three technical contributions to significantly enhance the performance of ECCT. First, we propose a novel transformer architecture of ECCT, termed themultiple-masks ECCT (MM ECCT). We employ multiple masked self-attention blocks with different mask matrices in a parallel manner to learn diverse relationships among the codeword bits. Second, we discover that constructing mask matrices based on systematic parity check matrices (PCMs) can make the attention mapssparse, which not only enhances the decoding performance but also reduces computational complexity. Finally, we propose using complementary mask matrices derived from cyclic permutations of the systematic PCM. These complementary mask matrices are specifically designed to enhance the decoding of cyclic codes. Our extensive simulation results show that the proposed MM ECCT architecture with carefully designed mask matrices outperforms the original ECCT by a large margin, achieving state-of-the-art decoding performance among neural decoders. The source code is available at https://github.com/iil-postech/mm-ecct.
Error correction codes (ECC) are crucial for ensuring reliable information transmission in communication systems. Choukroun & Wolf (2022b) recently introduced the Error Correction Code Transformer (ECCT), which has demonstrated promising performance across various transmission channels and families of codes. However, its high computational and memory demands limit its practical applications compared to traditional decoding algorithms. Achieving effective quantization of the ECCT presents significant challenges due to its inherently small architecture, since existing, very low-precision quantization techniques often lead to performance degradation in compact neural networks. In this paper, we introduce a novel acceleration method for transformer-based decoders. We first propose a ternary weight quantization method specifically designed for the ECCT, inducing a decoder with multiplication-free linear layers. We present an optimized self-attention mechanism to reduce computational complexity via codeaware multi-heads processing. Finally, we provide positional encoding via the Tanner graph eigendecomposition, enabling a richer representation of the graph connectivity. The approach not only matches or surpasses ECCT's performance but also significantly reduces energy consumption, memory footprint, and computational complexity. Our method brings transformer-based error correction closer to practical implementation in resource-constrained environments, achieving a 90% compression ratio and reducing arithmetic operation energy consumption by at least 224 times on modern hardware.
Neural decoders have recently advanced error correction performance, with transformer-based architectures in the error correction code transformer (ECCT) framework achieving state-of-the-art results among neural decoders. However, the multiple-masks ECCT suffers from suboptimal mask selection, which impacts decoding performance. In this work, we propose spectral-guided ECCT, leveraging the Laplacian matrix and its eigenvectors from the variable-variable graph to identify weakly connected node clusters for optimized mask generation. By embedding spectral properties into the decoding process, our method constructs more effective masks that improve information flow across variable and check nodes. Experimental results demonstrate consistent gains over existing ECCT-based models, achieving superior decoding accuracy and reliability while significantly improving training efficiency. This work highlights the potential of spectral graph theory to address structural challenges in neural decoders and provides a principled direction for future error correction design.
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.
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.
Channel coding is vital for reliable sixth-generation (6G) data transmission, employing diverse error correction codes for various application scenarios. Traditional decoders require dedicated hardware for each code, leading to high hardware costs. Recently, artificial intelligence (AI)-driven approaches, such as the error correction code Transformer (ECCT) and its enhanced version, the foundation error correction code Transformer (FECCT), have been proposed to reduce the hardware cost by leveraging the Transformer to decode multiple codes. However, their excessively high computational complexity ofO(N2) due to the self-attention mechanism in the Transformer limits scalability, whereNrepresents the sequence length. To reduce computational complexity, we propose a unified Transformer-based decoder that handles multiple linear block codes within a single framework. Specifically, a standardized unit is employed to align code length and code rate across different code types, while a redesigned low-rank unified attention module, with computational complexity ofO(N), is shared across various heads in the Transformer. Additionally, a sparse mask, derived from the parity-check matrix’s sparsity, is introduced to enhance the decoder’s ability to capture inherent constraints between information and parity-check bits, improving decoding accuracy and further reducing computational complexity by 86%. Extensive experimental results demonstrate that the proposed unified Transformer-based decoder outperforms existing methods and provides a high-performance, low-complexity solution for next-generation wireless communication systems.