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arXiv:2605.03620

Leveraging Code Automorphisms for Improved Syndrome-Based Neural Decoding

Raphaël Le Bidan, Ahmad Ismail, Elsa Dupraz, Charbel Abdel Nour

Published May 5, 2026• 0 citations
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Abstract

Syndrome-based neural decoding (SBND) has emerged as a promising deep learning approach for soft-decision decoding of high-rate, short-length codes. However, this approach still has substantial room for improvement. In this paper, we show how to leverage code automorphisms to enhance the ability of existing SBND models to learn and generalize through data augmentation during training and inference. As a result, for the short high-rate codes considered, we obtain models that closely approach MLD performance using small datasets and proper training. Our findings also suggest that many prior results for SBND models in the literature underestimate their true correction capability due to undertraining. Code to reproduce all results is available at: https://github.com/lebidan/sbnd.

DOI
10.48550/arxiv.2605.03620

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Syndrome-based neural decoding (SBND) has emerged as a promising deep learning approach for soft-decision decoding of high-rate, short-length codes. However, this approach still has substantial room for improvement. In this paper, we show how to leverage code automorphisms to enhance the ability of existing SBND models to learn and generalize through data augmentation during training and inference. As a result, for the short high-rate codes considered, we obtain models that closely approach MLD performance using small datasets and proper training. Our findings also suggest that many prior results for SBND models in the literature underestimate their true correction capability due to undertraining. Code to reproduce all results is available at: https://github.com/lebidan/sbnd.
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In this work, we introduce a framework that enables the use of Syndrome-Based Neural Decoders (SBND) for high-order Bit-Interleaved Coded Modulations (BICM). To this end, we extend the previous results on SBND, for which the validity is limited to Binary Phase-Shift Keying (BPSK), by means of a theoretical channel modeling of the bit Log-Likelihood Ratio (bit-LLR) induced outputs. We implement the proposed SBND system for two polar codes (64, 32) and (128, 64), using a Recurrent Neural Network (RNN) and a Transformer-based architecture. Both implementations are compared in Bit Error Rate (BER) performance and computational complexity.
In this work, we introduce a framework that enables the use of Syndrome-Based Neural Decoders (SBND) for high-order Bit-Interleaved Coded Modulations (BICM). To this end, we extend the previous results on SBND, for which the validity is limited to Binary Phase-Shift Keying (BPSK), by means of a theoretical channel modeling of the bit Log-Likelihood Ratio (bit-LLR) induced outputs. We implement the proposed SBND system for two polar codes (64,32)(64,32)(64,32) and (128,64)(128,64)(128,64), using a Recurrent Neural Network (RNN) and a Transformer-based architecture. Both implementations are compared in Bit Error Rate (BER) performance and computational complexity.
Error correction at short blocklengths remains a challenge for low-density parity-check (LDPC) codes, as belief propagation (BP) decoding is suboptimal compared to maximum-likelihood decoding (MLD). While BP rarely makes errors, it often fails to converge due to a small number of problematic, erroneous variable nodes (VNs). Multi-round BP (MRBP) decoding improves performance by identifying and perturbing these VNs, enabling BP to succeed in subsequent decoding attempts. However, existing heuristic approaches for VN identification may require a large number of decoding rounds to approach ML performance. In this work, we draw a connection between identifying candidate VNs to perturb in MRBP and estimating channel output errors, a problem previously addressed by syndrome-based neural decoders (SBND). Leveraging this insight, we propose an SBND-inspired neural network architecture that learns to predict which VNs MRBP needs to focus on. Experimental results demonstrate that the proposed learning approach outperforms expert rules from the literature, requiring fewer MRBP decoding attempts to reach near-MLD performance. This makes it a promising lead for improving the decoding of short LDPC codes.
We present a novel framework for applying deep neural networks (DNN) to soft decoding of linear codes at arbitrary block lengths. Unlike other approaches, our framework allows unconstrained DNN design, enabling the free application of powerful designs that were developed in other contexts. Our method is robust to overfitting that inhibits many competing methods, which follows from the exponentially large number of codewords required for their training. We achieve this by transforming the channel output before feeding it to the network, extracting only the syndrome of the hard decisions and the channel output reliabilities. We prove analytically that this approach does not involve any intrinsic performance penalty, and guarantees the generalization of performance obtained during training. Our best results are obtained using a recurrent neural network (RNN) architecture combined with simple preprocessing by permutation. We provide simulation results that demonstrate performance that sometimes approaches that of the ordered statistics decoding (OSD) algorithm.
This paper proposes a newly developed layer-wise syndrome-based framework for decoding Low-Density Parity-Check (LDPC) codes using deep learning. The framework leverages a layer-specific training approach to design methodologically effective decoding strategies, aiming to utilize the specific characteristics of each layer and improve overall decoding performance. By integrating the Normalized Offset Min-Sum (NOMS) algorithm into a Forward-Feedback Neural Network (NOMS-FF), the proposed model employs a soft-syndrome loss function to assist the learning of codeword structures and optimize decoding performance across varying noise levels. Additionally, the framework incorporates a layer-freezing strategy and dynamic Signal-to-Noise Ratio (SNR) allocation, enabling targeted post-training adjustments tailored to layer-specific characteristics. Experimental results on 6G-candidate QC-LDPC codes (Base Graph 2, N=240,K=80 ) demonstrate that the proposed approach provides substantial performance advantages over traditional decoders across the entire SNR range tested in this study. Furthermore, this study conducts partial-layer decoding experiments, which demonstrate that using only a subset of neural network layers can reduce the model’s computational runtime while simultaneously maintaining or improving decoding accuracy compared to the full-layer model under specific noise conditions.