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International Conference on Wireless Communications and Signal Processing (WCSP)

Multi-connection BP Decoding for Polar Codes

Liuchang Yang, Dianhong Wang, Zhongxiu Feng, Yangyang Liu, Lixia Xiao

Published Nov 1, 2022• 1 citation
Publisher

Abstract

In this paper, we develop a multi-connection belief propagation (BP) decoding algorithm for polar codes, which employs the idea of the residual neural network to accelerate the convergence. Specifically, multi-connection BP decoding builds on the standard BP decoding by fusing the soft information of the current decoding iteration and the past decoding iterations proportionally according to the damping factor during each iteration. Moreover, we adopt the particle swarm optimization algorithm to obtain the optimal value of the damping factor to balance a trade-off between the error rate performance and decoding complexity. The suggested approach can outperform the standard BP decoding with lower iterations, according to simulation findings, which demonstrate that it can reduce error rates.

DOI
10.1109/wcsp55476.2022.10039219

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In this paper, we develop a multi-connection belief propagation (BP) decoding algorithm for polar codes, which employs the idea of the residual neural network to accelerate the convergence. Specifically, multi-connection BP decoding builds on the standard BP decoding by fusing the soft information of the current decoding iteration and the past decoding iterations proportionally according to the damping factor during each iteration. Moreover, we adopt the particle swarm optimization algorithm to obtain the optimal value of the damping factor to balance a trade-off between the error rate performance and decoding complexity. The suggested approach can outperform the standard BP decoding with lower iterations, according to simulation findings, which demonstrate that it can reduce error rates.
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.
The polar neural decoder has a performance improvement at the cost of additional storage and computation. In this letter, we first propose a ResNet-like BP architecture to improve the standard polar BP decoding. Each iteration inherits a portion of information from the previous iteration as additional input and passes its output to the next iteration. Second, trainable damping factors, which can be learned through deep learning techniques, are applied to determine the inheritance ratio in the ResNet-like BP. We allocate the damping factors flexibly and demonstrate the optimization of a shared constant damping factor provides the same level of performance with the individual optimization of the damping factor at each state. Moreover, we qualitatively explain the performance gain by analyzing the mutual information between the input and output of the decoder. Numerical and simulation results indicate that the ResNet-like BP decoder can effectively improve the error correction performance and accelerate convergence compared with the standard polar BP algorithm.
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.
In recent years, the emerging Deep Learning (DL) technology has made progress in the field of decoding. Current polar code neural network decoder has faster convergence speed and better Bit Error Rate (BER) performance than Belief Propagation (BP) decoding. However, it still has the problem of high computational complexity. Therefore, in order to improve this problem, this paper adopts the idea of improving information update in the iterative process, and proposes a Recurrent Neural Network (RNN) Offset Min-Sum (OMS) BP decoding algorithm that improves Left information update (RNN-OMSBP-L) . The simulation results show that, compared with the Deep Neural Network (DNN) BP(DNN-BP) decoding algorithm, this algorithm replaces all multiplications with a cost of 6.25% addition. Compared with the current optimized RNN OMS and approximate BP(RNN-OMS-BP) decoding algorithm, the decoding algorithm in this paper uses improved information to reduce 25% of the addition operations with almost no loss in BER performance, while saving part of the storage space overhead. Under the same BER performance, it reduces the number of iterations by 37.5%.
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.
We propose a generalization belief propagation (BP) decoding algorithm based on particle swarm optimization (PSO) to improve the performance of the polar codes. Through the analysis of the existing BP decoding algorithm, we first introduce a probability modifying factor to each node of the BP decoder, so as to enhance the error correcting capacity of the decoding. Then, we generalize the BP decoding algorithm based on these modifying factors and drive the probability update equations for the proposed decoding. Based on the new probability update equations, we show the intrinsic relationship of the existing decoding algorithms. Finally, in order to achieve the best performance, we formulate an optimization problem to find the optimal probability modifying factors for the proposed decoding algorithm. Furthermore, a method based on the modified PSO algorithm is also introduced to solve that optimization problem. Numerical results show that the proposed generalization BP decoding algorithm achieves better performance than that of the existing BP decoding, which suggests the effectiveness of the proposed decoding algorithm.