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IEEE International Symposium on Information Theory (ISIT)

Section-Wise Revolving NBP-Like Decoders for QC-LDPC Codes

Qinshan Zhang, Bin Chen, Tianqu Zhuang, Yong Jiang, Shu‐Tao Xia

Published Jul 7, 2024• 4 citations
Publisher

Abstract

Recently, deep learning has demonstrated improvements over classical decoding algorithms in various families of error-correcting codes with short to moderate block lengths. Neural decoders like neural belief propagation (NBP), constructed based on the Tanner graphs of linear codes, have been extensively studied, but their application to longer codes is limited due to increased network complexity with longer block lengths. This complexity leads to higher computational costs and deployment challenges, such as GPU memory usage. To address this, we propose a novel revolving framework for NBP-like decoders tailored to QC-LDPC codes, a commonly used class of error correction codes. Our approach leverages the section-wise cyclic structure inherent in QC-LDPC codes, significantly simplifying the complexity of the network. Experimental results demonstrate the effectiveness of our method across various QC-LDPC codes. Especially, compared to the traditional decoding scheme based on the section-wise cyclic structure, our proposed decoder shows substantial improvements on 5G LDPC codes, exhibits better performance than the traditional min-sum decoder, and approaches the sum-product decoder without a noticeable error floor within the investigated noise levels.

DOI
10.1109/isit57864.2024.10619193

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For short to moderate-length block codes, neural belief propagation (NBP) decoders are developed to ameliorate the performance of the belief propagation algorithm (BPA). The core concept underlying these decoders is to model belief propagation (BP) as a neural network, allowing adaptable decoding through trainable weights. The article proposes a novel Gated neural min-sum (GNMS) decoding technique with learnable parameters as a more hardware-efficient substitute for conventional NBP decoders. By using parameterised updates and gating techniques, our approach reformulates the min-sum (MS) algorithm, which is an approximation of BP, while preserving the flexibility of neural approaches and drastically lowering computing overhead. Additionally, we develop an autoencoder-assisted framework that supports flexible, learning-based optimisation for GNMS and Gated Neural Offset Min-Sum (GNOMS) decoders. The suggested decoders achieve error-correction performance at par with the most advanced NBP decoders by evaluating them on a variety of short to moderate-length block codes. Notably, when compared to traditional BP, the suggested approach lowers the bit error rate (BER) 10-fold for signal-to-noise ratio (SNR) greater than 3 dB. Furthermore, the efficacy of the proposed work is exhibited by comparing the computational complexity of the neural network-based decoders, highlighting the advantages in terms of practical implementation and hardware feasibility. The simulation results demonstrate that GNMS decoding with learnable parameters offers a convincing trade-off between complexity and performance, offering a potential path for future decoder design in contemporary communication systems.
With the rapid development of deep learning research and physical layer communication applications, deep learning-based channel coding has gradually become a research hotspot. In this paper, we propose a LDPC decoding network based on neural belief propagation (NBP) decoding. By introducing weights sharing mechanism, the weights vary across different iterations. The number of parameters is reduced, which significantly lowers memory requirements. In addition, we optimize the loss function to better train the model, achieving a lower bit error rate (BER) performance. Experimental results show that the proposed decoder yields significant performance improvements with respect to NBP, and significantly reducing the number of learnable weights.
BP decoding algorithm is one of the commonly used decoding algorithms for LDPC codes. To adapt LDPC codes to different 5G scenarios and further improve the decoding performance of short LDPC codes, a scheme combining model-driven deep learning with a traditional BP decoding algorithm is proposed. With the advantages of model-driven, this solution expands the decoding iteration process between the check node and the variable node into a neural network and proposes a parameter normalization optimization solution to solve the problem of the program with many training parameters, the edge weights of the optimized Tanner graph are re-assigned and bound. Simulation results show that the proposed scheme can improve the decoding performance of LDPC codes with short lengths.
We consider near maximum-likelihood (ML) decoding of short linear block codes. In particular, we propose a novel decoding approach based on neural belief propagation (NBP) decoding recently introduced by Nachmani et al. in which we allow a different parity-check matrix in each iteration of the algorithm. The key idea is to consider NBP decoding over an overcomplete parity-check matrix and use the weights of NBP as a measure of the importance of the check nodes (CNs) to decoding. The unimportant CNs are then pruned. In contrast to NBP, which performs decoding on a given fixed parity-check matrix, the proposed pruning-based neural belief propagation (PB-NBP) typically results in a different parity-check matrix in each iteration. For a given complexity in terms of CN evaluations, we show that PB-NBP yields significant performance improvements with respect to NBP. We apply the proposed decoder to the decoding of a Reed-Muller code, a short low-density parity-check (LDPC) code, and a polar code. PB-NBP outperforms NBP decoding over an overcomplete parity-check matrix by 0.27-0.31 dB while reducing the number of required CN evaluations by up to 97%. For the LDPC code, PB-NBP outperforms conventional belief propagation with the same number of CN evaluations by 0.52 dB. We further extend the pruning concept to offset min-sum decoding and introduce a pruning-based neural offset min-sum (PB-NOMS) decoder, for which we jointly optimize the offsets and the quantization of the messages and offsets. We demonstrate performance 0.5 dB from ML decoding with 5-bit quantization for the Reed-Muller code.
We investigate the application of machine learning techniques (in particular, deep neural networks, DNN) to improve the decoding algorithms of short quasi-cyclic low-density paritycheck (LDPC) codes adopted to the 5G standard. We note that straightforward application of general-purpose DNNs is not possible due to the curse of dimensionality problem – the training set size grows exponentially with the number of information bits. In our opinion, the only way to deal with this problem is to combine deep learning methods with existing decoding algorithms. We start with a Tanner-based neural network decoder with Min-Sum activation functions proposed by Nachmani et al. and extend it as follows. First, the quasi-cyclic nature of 5G LDPC codes allows us to use a single weight per circular matrix (circulant). We refer to this as weight sharing. This idea significantly reduces the training time, preserving the error-correcting performance. Second, we add residual connections to our NN architecture. Residual connections improve the performance and reduce the training time. We also present the results for the rate and length adaptation techniques. Rate adaptation allows multiple DNNs corresponding to different coding rates to run with a single set of trained weights. Length adaptation allows optimally reusing weights for multiple lifting size indices.