Regularized Neural Network-Based Normalized Min-Sum Decoding for LDPC Codes

ZHOU Hua; ZHOU Ming; ZHANG Likang

doi:10.11999/JEIT240860

Volume 47 Issue 5

May 2025

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Article Navigation > Journal of Electronics & Information Technology > 2025 > 47(5): 1486-1493

ZHOU Hua, ZHOU Ming, ZHANG Likang. Regularized Neural Network-Based Normalized Min-Sum Decoding for LDPC Codes[J]. Journal of Electronics & Information Technology, 2025, 47(5): 1486-1493. doi: 10.11999/JEIT240860

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ZHOU Hua, ZHOU Ming, ZHANG Likang. Regularized Neural Network-Based Normalized Min-Sum Decoding for LDPC Codes[J]. Journal of Electronics & Information Technology, 2025, 47(5): 1486-1493. doi: 10.11999/JEIT240860

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Regularized Neural Network-Based Normalized Min-Sum Decoding for LDPC Codes

doi: 10.11999/JEIT240860 cstr: 32379.14.JEIT240860

ZHOU Hua^{1, 2
,
,},
ZHOU Ming¹,
ZHANG Likang¹

1.
School of Electronic and Information Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, China
2.
Jiangsu Collaborative Innovation Center on Atmospheric Environment and Equipment Technology, Nanjing 210044, China

Funds: The National Natural Science Foundation of China (62001238, 62201271)

Received Date: 2024-10-14
Rev Recd Date: 2025-03-28

Available Online: 2025-04-23

Publish Date: 2025-05-01

Abstract

Abstract

Objective The application of deep learning in communications has demonstrated significant potential, particularly in Low Density Parity Check (LDPC) code decoding. As a rapidly evolving branch of artificial intelligence, deep learning effectively addresses complex optimization problems, making it suitable for enhancing traditional decoding techniques in modern communication systems. The Neural-network Normalized Min-Sum (NNMS) algorithm has shown improved performance over the Min-Sum (MS) algorithm by incorporating trainable neural network models. However, NNMS decoding assigns independent training weights to each edge in the Tanner graph, leading to excessive training complexity and high storage overhead due to the large number of weight parameters. This significantly increases computational demands, posing challenges for implementation in resource-limited hardware. Moreover, the excessive number of weights leads to overfitting, where the model memorizes training data rather than learning generalizable features, degrading decoding performance on unseen codewords. This issue limits the practical applicability of NNMS-based decoders and necessitates advanced regularization techniques. Therefore, this study explores methods to reduce NNMS decoding complexity, mitigate overfitting, and enhance the decoding performance of LDPC codes. Methods Building on the traditional NNMS decoding algorithm, this paper proposes two partially weight-sharing models: VC-SNNMS (sharing weights for edges from variable nodes to check nodes) and CV-SNNMS (sharing weights for edges from check nodes to variable nodes). These models apply a weight-sharing strategy to specific edge types in the bipartite graph, reducing the number of training weights and computational complexity. To mitigate neural network overfitting caused by the high complexity of NNMS and its variants, a regularization technique is proposed. This leads to the development of the Regularized NNMS (RNNMS), Regularized VC-SNNMS (RVC-SNNMS), and Regularized CV-SNNMS (RCV-SNNMS) algorithms. Regularization refines network parameters by modifying the loss function and gradients, penalizing excessively large weights or redundant features. By reducing model complexity, this approach enhances the generalization ability of the decoding neural network, ensuring robust performance on both training and test data. Results and Discussions To evaluate the effectiveness of the proposed algorithms, extensive simulations are conducted under various Signal-to-Noise Ratio (SNR) conditions. The performance is assessed in terms of Bit Error Rate (BER), decoding complexity, and convergence speed. Additionally, a comparative analysis of NNMS, SNNMS, VC-SNNMS, and CV-SNNMS, and their regularized variants systematically examines the effects of weight-sharing and regularization on neural network-based decoding. Simulation results show that for an LDPC code with a block length of 576 and a code rate of 0.75, when BER = 10^–6, the RNNMS, RVC-SNNMS, and RCV-SNNMS algorithms achieve SNR gains of 0.18 dB, 0.22 dB, and 0.27 dB, respectively, compared to their corresponding NNMS, VC-SNNMS, and CV-SNNMS algorithms. Notably, the RVC-SNNMS algorithm demonstrates the best performance, with SNR gains of 0.55 dB, 0.51 dB, and 0.22 dB compared to the BP, NNMS, and SNNMS algorithms, respectively (Fig. 3). Furthermore, under different numbers of decoding iterations, the RVC-SNNMS algorithm consistently outperforms the others in BER performance. Specifically, at BER = 10^–6 with 15 decoding iterations, it achieves SNR gains of 0.57 dB and 0.1 dB compared to the NNMS and SNNMS algorithms, respectively (Fig. 4). Similarly, for an LDPC code with a block length of 1056, when BER = 10^–5 and 10 decoding iterations are used, the RVC-SNNMS algorithm attains SNR gains of 0.34 dB and 0.08 dB compared to the NNMS and SNNMS algorithms, respectively (Fig. 5). Conclusions This study investigates the performance of NNMS and SNNMS for LDPC code decoding and proposes two partially weight-sharing algorithms, VC-SNNMS and CV-SNNMS. Simulation results show that weight-sharing strategies effectively reduce training complexity while maintaining competitive BER performance. To address the overfitting issue associated with the high complexity of NNMS-based algorithms, regularization is incorporated, leading to the development of RNNMS, RVC-SNNMS, and RCV-SNNMS. Regularization effectively mitigates overfitting, enhances network generalization, and improves error-correcting performance for various LDPC codes. Simulation results indicate that the RVC-SNNMS algorithm achieves the best decoding performance due to its reduced complexity and the improved generalization provided by regularization.
- Low Density Parity Check (LDPC) codes,
- Neural network,
- Normalized min-sum decoding,
- Overfitting,
- Regularization

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References(20)

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