With the success of transformer architectures across diverse applications, the error correction code transformer (ECCT) has gained significant attention for its superior decoding performance. In spite of its advantages, the error floor problem in ECCT decoding remains unexplored. We present the first investigation into this issue, revealing that ECCT encounters error floors, limiting its effectiveness in practical settings. To address this error floor problem, we adopt a hybrid decoding framework that integrates ECCT with conventional hard decision decoders. Unlike prior hybrid decoding schemes, our key contribution lies in proposing a novel loss function that explicitly takes into account the interaction between ECCT and hard decision decoders during training. The proposed loss function guides ECCT to focus on residual errors that are not corrected by the hard decision stages, effectively lowering the error floor. Simulation results confirm that the hybrid decoder trained with the proposed loss function achieves substantial performance gains over standard ECCT in both the waterfall and the error floor regions.
With the success of transformer architectures across diverse applications, the error correction code transformer (ECCT) has gained significant attention for its superior decoding performance. In spite of its advantages, the error floor problem in ECCT decoding remains unexplored. We present the first investigation into this issue, revealing that ECCT encounters error floors, limiting its effectiveness in practical settings. To address this error floor problem, we adopt a hybrid decoding framework that integrates ECCT with conventional hard decision decoders. Unlike prior hybrid decoding schemes, our key contribution lies in proposing a novel loss function that explicitly takes into account the interaction between ECCT and hard decision decoders during training. The proposed loss function guides ECCT to focus on residual errors that are not corrected by the hard decision stages, effectively lowering the error floor. Simulation results confirm that the hybrid decoder trained with the proposed loss function achieves substantial performance gains over standard ECCT in both the waterfall and the error floor regions.
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.
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.
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.
Transformer channel decoders, such as the Error Correction Code Transformer (ECCT), have shown strong empirical performance in channel decoding, yet their generalization behavior remains theoretically unclear. This paper studies the generalization performance of ECCT from a learning-theoretic perspective. By establishing a connection between multiplicative noise estimation errors and bit-error-rate (BER), we derive an upper bound on the generalization gap via bit-wise Rademacher complexity. The resulting bound characterizes the dependence on code length, model parameters, and training set size, and applies to both single-layer and multi-layer ECCTs. We further show that parity-check-based masked attention induces sparsity that reduces the covering number, leading to a tighter generalization bound. To the best of our knowledge, this work provides the first theoretical generalization guarantees for this class of decoders.
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.
In this work, we introduce two variants of the U-shaped error correction code transformer (U-ECCT) in combination with weight-sharing to improve the decoding performance of the error correction code transformer (ECCT) for moderate-length linear codes. The proposed models are inspired by the well-known U-Net architecture to leverage residual information for faster error estimation based on the syndrome-based reliability decoding principle. As an effort to further improve the general decoding performance of the U-ECCT, we propose the variational U-ECCT (VU-ECCT), in which the process of learning the shortcut connections is treated as a generative problem, forming a variational autoencoder (VAE) that exists intertwined with the existing U-ECCT model. This design allows the extraction of mutual information between the different levels of the U-shaped architecture, thus enhancing the performance of large syndrome sequences for low-rate codes. Additionally, to further reduce the model size, a new weight-sharing strategy, called mirror-sharing, is proposed to compress the model size as well as complement the mechanism of the proposed U-shaped architecture. In experiments, it has been demonstrated that our proposed models achieve significantly better performance than baseline conventional algorithms and other learning-based models.