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IEEE Transactions on Cognitive Communications and Networking

Normalized Min-Sum Neural Network for LDPC Decoding

Qing Wang, Qing Liu, Shunfu Wang, Leian Chen, Haoyu Fang, Luyong Chen, Yuzhang Guo, Zhiqiang Wu

Published Oct 6, 2022• 31 citations
Publisher

Abstract

The success of deep learning has encouraged its applications in decoding error-correcting codes, e.g., LDPC decoding. In this paper, we propose a model-driven deep learning method for normalized min-sum (NMS) low-density parity-check (LDPC) decoding, namely neural NMS (NNMS) LDPC decoding network. By unfolding the iterative decoding progress between checking nodes (CNs) and variable nodes (VNs) into a feed-forward propagation network, we can harvest the benefits of both the model-driven deep learning and the conventional normalized min-sum (NMS) LDPC decoding method. In addition, we proposed a shared parameters NNMS with the LeakyReLU and a 12-bit quantizer (SNNMS-LR-Q) which reduces the number of required multipliers and correction factors by sharing parameters, increasing the nonlinear fitting ability by adding LeakyReLU. By utilizing the 12-bit quantizer, we can improve the confrontation ability. Thorough experiments with different code lengths, code rates, channel conditions, and check matrices are implemented to demonstrate the advantages and robustness of our proposed networks. The BER performance of the proposed NNMS is 1.5 dB better than the NMS, using fewer iterations. Meanwhile, The SNNMS-LR-Q outperforms the NNMS regarding the BER performance and efficiency.

DOI
10.1109/tccn.2022.3212438

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The success of deep learning has encouraged its applications in decoding error-correcting codes, e.g., LDPC decoding. In this paper, we propose a model-driven deep learning method for normalized min-sum (NMS) low-density parity-check (LDPC) decoding, namely neural NMS (NNMS) LDPC decoding network. By unfolding the iterative decoding progress between checking nodes (CNs) and variable nodes (VNs) into a feed-forward propagation network, we can harvest the benefits of both the model-driven deep learning and the conventional normalized min-sum (NMS) LDPC decoding method. In addition, we proposed a shared parameters NNMS with the LeakyReLU and a 12-bit quantizer (SNNMS-LR-Q) which reduces the number of required multipliers and correction factors by sharing parameters, increasing the nonlinear fitting ability by adding LeakyReLU. By utilizing the 12-bit quantizer, we can improve the confrontation ability. Thorough experiments with different code lengths, code rates, channel conditions, and check matrices are implemented to demonstrate the advantages and robustness of our proposed networks. The BER performance of the proposed NNMS is 1.5 dB better than the NMS, using fewer iterations. Meanwhile, The SNNMS-LR-Q outperforms the NNMS regarding the BER performance and efficiency.
With the applications of deep learning networks booming in physical layer communication, deep-learning-based channel decoding methods have become a research hotspot. However, the high complexity hinders the application of deep neural network (DNN) on long code. In this paper, we propose a model-driven deep learning method for normalized min-sum (NMS) low-density parity-check (LDPC) decoding. First, we propose a neural normalized min-sum (NNMS) LDPC decoding network. By unfolding the iterative decoding progress between checking nodes (CNs) and variable nodes (VNs) into a feedforward propagation network, we can make use of the advantages of both model-driven deep learning methods and conventional normalized min-sum (CNMS) LDPC decoding method. Second, considering that the NNMS decoder needs large number of multipliers, we propose a shared neural normalized min-sum (SNNMS) decoding network to reduce the number of correction factors. Experimental results show that the BER performance of the proposed NNMS decoder is 1.5dB better than the conventional LDPC decoder, using fewer iterations. Furthermore, the proposed SNNMS decoder outperforms the proposed NNMS decoder and reduces the computation complexity.
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.
Low-density parity-check (LDPC) codes are of prime importance in achieving near-Shannon capacity in current communication systems. However, the optimal decoding process for LDPC codes is computationally intensive. This paper presents a neural normalized min-sum (NNMS) decoding network that improves error correction capabilities with minimal computational overhead. A weight-sharing approach is adopted in the NNMS model, in which the correction factors (α, β) are shared across nodes within a single layer. This approach decreases the total number of parameters in the model compared to traditional neural decoders, making it easier for hardware implementation. The NNMS model is tested using a (576, 432) LDPC code for an additive white Gaussian noise channel with binary phase shift keying modulation. Simulation results show that the NNMS model outperforms traditional normalized min-sum (NMS) decoders. At a signal-to-noise ratio of 5 dB, the NNMS model has a bit-error rate (BER) of 1.0 × 10−7, whereas traditional NMS models have a less steep slope. In particular, the NNMS model has a coding gain of 1.25 dB compared to the traditional NMS model at a BER threshold of 1.0 × 10−3. This shows that the NNMS model is an efficient solution for high-performance, real-time digital communication systems.
For recent years, deep learning has been studied and utilized among decoders in wireless and optical communication. For low density parity check (LDPC) codes, most works use neural network (NN) to implement the belief propagation (BP) decoder and unfold its iterations into layers activated by different functions. However, the whole decoder composed by neural network performs lots of non-linear operations, which are time consuming and unfriendly to hardware implementation. In this work, a neural network-aided normalized min-sum (NN-aided NMS) decoder for LDPC code is proposed, in which the normalization factors are inferred from input log likelihood ratio (LLR) by apre-trained NN, while maintaining check and variable nodes processing the same as in min-sum (MS) decoder. In order to test the proposed decoder with irregular LDPC code, a rate-7/8 one was constructed using progressive edge growth (PEG) algorithm, showing better error correction capability than the standard of consultative committee for space data systems (CCSDS) LDPC (8176,7154) code by 0.08 dB with the same rate. Simulation results show that, NN-aided NMS decoder outperforms MS decoder by 0.3 dB, and its performance approaches BP decoder with a gap of 0.02 dB, which is 50% closer than the best NMS decoder using 0.7 as the normalization factor. The proposed decoder has good performance for both regular and irregular LDPC codes, and needs much less computation complexity than BP decoder. It introduces more linear computation than NMS decoder but achieves better bit error rate (BER) performance, thus becoming a good complement between BP and NMS decoder when trading off among complexity, error correction performance and hardware implementation for wireless and satellite communication.
Compared with traditional low-density parity-check (LDPC) decoding algorithms, the current model-driven deep learning (DL)-based LDPC decoding algorithms face the disadvantage of high computational complexity. Based on the Neural Normalized Min-Sum (NNMS) algorithm, we propose a low-complexity model-driven DL-based LDPC decoding algorithm using Tensor-Train (TT) decomposition and syndrome loss function, called TT-NNMS+ algorithm. Our experiments show that the proposed TT-NNMS+ algorithm is more competitive than the NNMS algorithm in terms of bit error rate (BER) performance, memory requirement and computational complexity.
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.