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A Layer-Wise Syndrome-Based Framework for LDPC Decoding with Deep Learning

Ziwen Ren

Published Jan 1, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.65286/icic.v22i2.13234

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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.
With the rapid development of deep learning and its applications in physical layer communication, deep learning-based channel coding has gradually become a research hotspot. In this paper, based on the neural offset min-sum (NOMS) low-density parity-check (LDPC) decoding network, we propose a neural adaptive offset min-sum (NAOMS) LDPC decoding network. By considering the current input values of the check nodes when learning the additive offset parameters and introducing an adaptive offset weight vector, we can better leverage deep learning techniques. Experimental results show that, with a slight increase in complexity, the proposed decoder achieves a 0.8dB improvement in bit error rate (BER) over the NOMS LDPC decoding network. Moreover, the NAOMS decoder requires fewer learning offset parameters compared to the NOMS decoder.
In this letter, we propose various low-complexity neural layered min-sum (NLMS) algorithms to improve the decoding performance of the fifth generation (5G) new radio (NR) low-density parity-check (LDPC) codes. Our proposals are based on the computationally-efficient normalized offset min-sum (NOMS) approach for the layered belief propagation (LBP). The main novelty of our proposals is a deep neural network (DNN) that implements the layered mode decoding and that additionally learns the normalization and the offset parameters of the NOMS scheme. The schemes that we propose use the DNN as well as adaptation and filtering for estimating the optimum values of these parameters. We show by simulation that our proposed decoders achieve a significant computational benefit compared to the standard (non-neural) LBP decoder without an appreciable performance penalty.
A novel Neural Offset Min-Sum(NOMS) Belief Propagation(BP) decoding algorithm based on model-driven is proposed which applied to LDPC decoding. NOMS is improved multiplication in Neural Normalized Min-Sum(NNMS) into addition operation to reduce the complexity of calculation., a better Bit Error Rate (BER) performance is simultaneously achieved in the same condition. Secondly, considering that there are still many multiplication operations in NOMS, we propose a novel Shared Offset Min-Sum(SNOMS) to reduce the number of weights in the network by sharing parameters. Finally, codebook-based quantization is used to further reduce the memory consumption. Simulation experimental results show that the proposed method has a better BER performance, and the decoding accuracy of the decoder is 0.65dB higher than that of the NNMS after 5 iterations. In addition, SNOMS decoding method achieves almost the same decoding performance comparable to that of NOMS, but requires less complex calculation. Proposed quantization of code-book method reduces memory requirement significantly with slight performance loss.
Low-density parity-check (LDPC) codes are widely used in a variety of communication systems because of their low complexity iterative decoding and performance approaching Shannon capacity. However, the existence of error floor seriously hinders the application and development of LDPC codes in related fields. In this paper, a deep learning-aided post-processing scheme (DLAPPS) based on Layered Normalized Min-Sum algorithm (LNMSA) is proposed to effectively lower error floor of LDPC codes. LNMSA is used in the first stage, and in the second stage incorrect frames are re-decoded by processing two types of nodes classified by neural networks. Simulation results show that the proposed DLAPPS can significantly improve error correction performance and lower the error floor of LDPC codes while maintaining a relatively low decoding complexity.
This thesis investigates the optimization of Low-Density Parity-Check (LDPC) decoding through machine learning techniques, with a specific focus on 5G communication systems. Traditional LDPC decoding algorithms face a critical trade-off: Belief Propagation (BP) offers excellent error-correction performance but with high computational complexity, while Min-Sum (MS) reduces complexity at the cost of degraded performance. To address this limitation, a hybrid neural network architecture is proposed that incorporates learnable normalization and offset weights into the message-passing framework of LDPC decoders. This approach integrates multiplicative (normalization) and additive (offset) weights into the Tanner graph structure, allowing the decoder to adapt to specific channel conditions. A novel weighted binary cross-entropy loss function is developed that prioritizes entire block recovery by assigning different importance to information and parity bits during training. Experimental results demonstrate that ML-assisted decoder consistently outperforms conventional Min-Sum decoding, approaching the error-correction capability of Belief Propagation while maintaining comparable computational efficiency to Min-Sum. Comprehensive evaluations across different weight configurations (scalar and vector-based) reveal that increased parametrization generally improves decoding performance. Analysis of the impact of iteration counts shows that the optimal number of decoding iterations varies between different code configurations with studied Basegraph 1 case requiring 15 iterations for optimal performance while studied Basegraph 2 case benefits significantly from 20 iterations. The proposed ML-assisted LDPC decoder represents a significant advancement for 5G systems, offering improved error correction at lower signal strengths while balancing latency and computational requirements. This research contributes to the ongoing evolution of wireless technology by demonstrating how machine learning can effectively enhance traditional decoding algorithms, providing a practical pathway toward more efficient and adaptive error correction in modern communication systems.
LDPC code is a widely-used high-performance error correction code. In recent years, LDPC decoding based on deep learning and neural networks becomes a research hotspot. Based on the (512,256) LDPC code of the CCSDS standard, this paper firstly studies the traditional decoding algorithms of SP, MS, NMS, and OMS, laying a foundation for the construction of neural networks. Then a data-driven (DD) decoding method is studied which adopts the information with its encoded, modulated and noise-added LDPC code as the training data within a Multi-layer Perceptron (MLP) neural network. In order to solve the problem of high bit error rate (BER) in data-driven method, the Neural Normalized Min-sum (NNMS) decoding in which the NMS algorithm is mapped to the neural network structure is proposed, achieving more excellent BER performance than that of NMS. The BER declines by 85.19% when channel SNR equals to 3.5 dB. Finally, improved training methods to enhance the SNR generalization ability of the NNMS network is studied.