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IEEE Symposium on Computers and Communications (ISCC)

A Model-Driven Quasi-ResNet Belief Propagation Neural Network Decoder for LDPC Codes

Liangsi Ma, Bei Liu, Xin Su, Xibin Xu

Published Jul 9, 2023• 1 citation
Publisher

Abstract

For the Belief Propagation (BP) algorithm of low-density parity-check (LDPC) codes, existing deep learning methods have a limited performance improvement and it is difficult to train deep-level networks. In this paper, a model-driven quasi-residual network (Quasi-ResNet) BP decoding architecture is proposed for LDPC codes to further improve the performance of standard BP decoding. This method feeds the reliable messages calculated in current iteration into the next iteration based on the shortcut connection, and adjusts the weight of shortcut connection based on the error Back Propagation algorithm of neural network to determine the optimal genetic proportion of reliable messages. The decoding architecture is composed of a model-driven deep neural network (DNN) and shortcut connection. Simulation results show that the decoder can not only unfold more layers quickly compared with the DNN-based BP decoder, but also further improve the decoding performance.

DOI
10.1109/iscc58397.2023.10217911

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For the Belief Propagation (BP) algorithm of low-density parity-check (LDPC) codes, existing deep learning methods have a limited performance improvement and it is difficult to train deep-level networks. In this paper, a model-driven quasi-residual network (Quasi-ResNet) BP decoding architecture is proposed for LDPC codes to further improve the performance of standard BP decoding. This method feeds the reliable messages calculated in current iteration into the next iteration based on the shortcut connection, and adjusts the weight of shortcut connection based on the error Back Propagation algorithm of neural network to determine the optimal genetic proportion of reliable messages. The decoding architecture is composed of a model-driven deep neural network (DNN) and shortcut connection. Simulation results show that the decoder can not only unfold more layers quickly compared with the DNN-based BP decoder, but also further improve the decoding performance.
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 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.
Today's modern wireless communication systems demand extensive quality and computational power with an increase in day-to-day data-rate standards. The latest com-munication standards focus on low latency, high throughput, and reliable error correction capabilities which inspired us to explore the 5G New Generation (NR) technology. Low-Density Parity-Check Codes (LDPC) are known to have error correction capabilities that can achieve Shannon's maximum channel ca-pacity. Encoding of LDPC Codes features a sparse property that enables effortless decoding at the receiver end. Advancements in deep learning have helped in estimating the channel noise more accurately. The Iterative Belief Propagation-Convolutional Neural Network (BP-CNN) architecture involves a CNN block which is trained with a quadratic loss function concatenated to a standard BP Decoder. The proposed Iterative BP-CNN architecture with a Batch Normalization layer results in a better performance compared to the Iterative BP-CNN architecture as it standardizes the input to the CNN block and also solves the problem of vanishing gradients during backpropagation.
LDPC codes, as an error correcting code close to the Shannon limit, are widely used in modern communication systems such as 5 G, satellite communication, deep space communication, and other fields. Traditional LDPC decoding algorithms, such as belief propagation (BP) algorithm and its variants, have achieved good performance, but face challenges such as high complexity and slow convergence, especially when dealing with long code lengths and high noise scenarios. The rise of deep learning has brought new opportunities for LDPC decoding, and its powerful features learning and pattern recognition capabilities are expected to break through the bottleneck of traditional decoding. Based on the overview of deep neural network decoding methods for LDPC codes by data-driven and model driven approaches, this paper analysis and comparison of error rate performance of short codeH(8,16)\mathbf{H} (8,16)H(8,16)matrix by convolutional neural networks (CNN), residual network (ResNet), and Kolmogorov-Arnold Network (KAN).
The neural networks offer iteration capability for low-density parity-check (LDPC) decoding with superior performance at transmission. However, to cope with increasing code length and rate, the complexity of the neural network increases significantly. This is due to the large amount of feature extraction required to maintain the error correction capability. Based on this gap, we design a new iterative LDPC decoding technique named graph model neural network-belief propagation (GMNN-BP). GMNN-BP uses graph models as a link between deep learning and belief propagation (BP) algorithms, combining the advantages of both. Compared to traditional fully connected neural network decoders, the GMNN-BP decoding has the substantial benefit of avoiding learning and judging codeword categories directly from a large amount of data and requiring less training data as well. The proposed algorithm is verified by simulation and experiment and is tested by using IEEE 802.3ca standard LDPC code word. The results show that the GMNN-BP decoding algorithm is superior to the BP-based iterative decoding method under the same number of iterations, and the maximum gain can reach 1.9dB. When achieving the same performance, the GMNN-BP decoding algorithm only requires half the number of iterations of other algorithms.
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.