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IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC)

A Sparse Neural Network Decoder for Non-binary Polar Codes

Yaofeng Shu, Hui Zhao, Changhao Han

Published Sep 12, 2022• 1 citation
Publisher

Abstract

Compared with binary Polar codes, non-binary Polar codes exhibit better performance, which is suitable for short packet services of Internet of Things. But its decoding complexity is high$(O(2N\log_{2}(N))$, where$N$is the length of the symbol sequence). To make it practical, this paper proposes a sparse neural network (SNN) decoder. Firstly, the Polar factor graph is transformed into a bipartite graph which contains variable node and check node. Then, we propose a pruning algorithm to prune the bipartite graph so as to get a sparse graph. After that, the sparse graph is expanded to get the structure of the deep neural network. Optimized by the training of deep learning, the proposed SNN decoding scheme has competitive performance to the traditional Belief-Propagation (BP) decoding scheme. Moreover, the SNN decoder achieves a reduction of 51.7% in the number of connections compared with BP decoding scheme and its decoding latency is significantly lower than the traditional BP.

DOI
10.1109/pimrc54779.2022.9978059

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Compared with binary Polar codes, non-binary Polar codes exhibit better performance, which is suitable for short packet services of Internet of Things. But its decoding complexity is high(O(2Nlog⁡2(N))(O(2N\log_{2}(N))(O(2Nlog2​(N)), whereNNNis the length of the symbol sequence). To make it practical, this paper proposes a sparse neural network (SNN) decoder. Firstly, the Polar factor graph is transformed into a bipartite graph which contains variable node and check node. Then, we propose a pruning algorithm to prune the bipartite graph so as to get a sparse graph. After that, the sparse graph is expanded to get the structure of the deep neural network. Optimized by the training of deep learning, the proposed SNN decoding scheme has competitive performance to the traditional Belief-Propagation (BP) decoding scheme. Moreover, the SNN decoder achieves a reduction of 51.7% in the number of connections compared with BP decoding scheme and its decoding latency is significantly lower than the traditional BP.
In this paper, we present a sparse neural network decoder (SNND) of polar codes based on belief propagation (BP) and deep learning. At first, the conventional factor graph of polar BP decoding is converted to the bipartite Tanner graph similar to low-density parity-check (LDPC) codes. Then the Tanner graph is unfolded and translated into the graphical representation of deep neural network (DNN). The complex sum-product algorithm (SPA) is modified to min-sum (MS) approximation with low complexity. We dramatically reduce the number of weight by using single weight to parameterize the networks. Optimized by the training techniques of deep learning, proposed SNND achieves comparative decoding performance of SPA and obtains about 0.5 dB gain over MS decoding on (128,64) and (256,128) codes. Moreover, 60% complexity reduction is achieved and the decoding latency is significantly lower than the conventional polar BP.
We describe a novel approach to interpret a polar code as a low-density parity-check (LDPC)-like code with an underlying sparse decoding graph. This sparse graph is based on the encoding factor graph of polar codes and is suitable for conventional belief propagation (BP) decoding. We discuss several pruning techniques based on the check node decoder (CND) and variable node decoder (VND) update equations, significantly reducing the size (i.e., decoding complexity) of the parity-check matrix. As a result, iterative polar decoding can then be conducted on a sparse graph, akin to the traditional well-established LDPC decoding, e.g., using a fully parallel sum-product algorithm (SPA). This facilitates the systematic analysis and design of polar codes using the well-established tools known from analyzing LDPC codes. We show that the proposed iterative polar decoder has a negligible performance loss for short-to-intermediate codelengths compared to Arikan's original BP decoder. Finally, the proposed decoder is shown to benefit from both reduced complexity and reduced memory requirements and, thus, is more suitable for hardware implementations.
Deep learning recently shows strong competitiveness to improve polar code decoding. However, suffering from prohibitive training and computation complexity, the conventional deep neural network (DNN) is only possible for very short code length. In this paper, the main problems of deep learning in decoding are well solved. We first present the multiple scaled belief propagation (BP) algorithm, aiming at obtaining faster convergence and better performance. Based on this, deep neural network decoder (NND) with low complexity and latency, is proposed for any code length. The training only requires a small set of zero codewords. Besides, its computation complexity is close to the original BP. Experiment results show that the proposed (64,32) NND with 5 iterations achieves even lower bit error rate (BER) than the 30-iteration conventional BP and (512, 256) NND also outperforms conventional BP decoder with same iterations. The hardware architecture of basic computation block is given and folding technique is also considered, saving about 50% hardware cost.
Polar code is selected for the 5-th generation of wireless communication standard. Meanwhile, with the demand of low latency in 5G and great success in deep learning area, neural network decoder (NND) becomes a promising candidate for future decoder. However, NND is currently only feasible for very short code lengths. In this paper, we proposed a belief propagation-neural network (BP-NN) algorithm for polar codes based on partitioning. The core of our algorithm is replacing subblock of belief propagation (BP) decoder with NNDs, and using BP decoding framework to connect them. In addition, we also introduce a weight function to complete the message propagation process. Simulation results show the proposed algorithm reduces the decoding delay compared to the traditional BP algorithm and have a well bit error rate (BER) performance. At the same time, it also suitable for long polar codes.
For the scenarios with high throughput requirements, the belief propagation (BP) decoding is one of the most promising decoding strategies for polar codes. By pruning the redundant variable nodes (VNs) and check nodes (CNs) in the original factor graph, the graph is condensed to a sparse bipartite graph which is similar to the graph for low-density parity-check (LDPC) codes. In this paper, we introduce the bit-flipping scheme into the LDPC-like BP (L-BP) decoding and propose two methods to identify the error-prone VNs. By additional decoding attempts, the L-BP flip (L-BPF) decoding improves the error-rate performance with a similar average complexity for high Eb=N0values. The simulation results show that the L-BPF decoding achieves 0:25 dB gain compared with the L-BP decoding.
With the development of communication technology, it is urgent to design channel decoding algorithms to maximize the high throughput and minimize the latency. As the capacity achieving polar codes are adopted by 5-th generation wireless system (5G), it is required to design efficient the decoding algorithms for polar codes with high performance and low complexity. Deep neural network (DNN)-based algorithms which have shown superiority in other fields, can obtain better performance using multi-scale belief propagation (BP) algorithm, whereas the decoding complexity needs to be decreased. We propose a residual neural network based belief propagation (ResNet- BP) algorithm to solve the inherent drawbacks in the existing methods, by reducing the number of variables in the network and reducing the complexity in terms of multiplication. Simulation results demonstrate that the proposed method can achieve the approximating performance of recurrent neural network-based belief propagation (RNN-BP) with a lower number of iterations.