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Mathematical Problems in Engineering

A Generalization Belief Propagation Decoding Algorithm for Polar Codes Based on Particle Swarm Optimization

Yingxian Zhang, Aijun Liu, Xiaofei Pan, Shi He, Chao Gong

Published Jan 1, 2014• 5 citations
Publisher

Abstract

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.

DOI
10.1155/2014/606913

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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.
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.
Abstract In order to solve the high latency problem of polar codes belief propagation decoding algorithm in the 5G and the dimension limitation problem of belief propagation decoding algorithm under deep learning, a multilayer perceptron belief propagation decoding (MLP-BP) algorithm based on partitioning idea is proposed. In this work, polar codes is decoded using neural networks in partitioning, and the right transfer message value of BP decoding algorithm is also set to complete the propagation process. Simulation results show that, compared with BP decoding algorithm, the proposed algorithm has better decoding performance, reducing the decoding latency, and it is also applicable to long polar codes.
Message-Passing is the main decoding algorithm for Low-Density Parity Check (LDPC) Codes, in which Logarithmic Belief Propagation (Log-BP) algorithm is the most popularly used one. Particle Swarm Optimization (PSO) can also be regarded as an optimization algorithm by message-passing, which makes it possible to combine Log-BP algorithm with PSO. PSO was introduced into Log-BP algorithm by regarding all messages that bit nodes send to check nodes as the swarm with each message individually as a particle. Move the particles around in the search-space by certain iterations in each BP iteration processing, guided by the two best current values respectively found by particles themselves and that of the whole swarm. Those two best values were continually updated in each PSO iteration. In this way, the output of decoder is more consistent with accurate input sequence, in other words, the decoder performance was improved. Simulation results show that this new algorithm combined with Log-BP and PSO can get an additional 0.1 dB coding gain at Bit Error Rate (BER) of 10-5compared with Log-BP algorithm.
In this study, a serially concatenated scheme of polar codes with convolutional codes is proposed to improve the error correction performance. The novel belief propagation (BP) decoding algorithm addresses two issues that are present in the currently available BP decoding algorithms. The first issue is the poor performance of the BP decoding algorithms, in particular the introduction of an error floor. The second is the component codes can only use systematic codes in the traditional concatenated scheme of polar codes with convolutional codes, which inhibits the effective update of the prior information of the redundant check bits. The proposed BP decoding algorithm is based on right‐directed message processing, which effectively improves the decoding performance. In addition, the proposed concatenated scheme extends the selection of component codes from the systematic polar codes to the non‐systematic polar codes. Hence, the areas of applications and the prior information of information bits for polar codes are expanded and more effectively updated, respectively. The simulation results show that the proposed scheme is much better than the traditional concatenated scheme, and the error floor is no longer introduced in terms of the block error rate, while the storage and computational complexities have not increased obviously.
A novel belief propagation(BP) decoding algorithm for convolutional low-density parity-check codes is proposed.The proposed algorithm raises the efficiency of updating the variable information by applying feedback information at each decoding iteration and employs the weighting factor to reduce the error propagation caused by the cycles in the Tanner graph,thus yielding a faster convergence of the decoding.Simulation results show that an error performance better than that of the existing belief propagation algorithm can be achieved,while the 5/8 decoding delay and the computation complexity are effectively reduced.Compared with the existing BP,the proposed algorithm achieves a gain of 0.16dB at the BER of 10-6 with the same number of iterations.
Belief propagation (BP) decoding for polar codes has been extensively studied because of its inherent parallelism. However, its performance remains inferior to that of successive cancellation list decoding (SCL) due to the structure of the decoding graph. To improve the block error rate (BLER) performance, the BP correction (BPC) decoding, a post-processing scheme that corrects prior knowledge of the identified code bit, improves convergence by executing additional iterations on the failed BP decoder. Moreover, the BPC decoder demonstrates a better decoding performance than the BP-based bit-flipping decoder. Nevertheless, the additional decoding attempts lead to increased latency. In this article, a modified BPC decoder is proposed to reduce the number of decoding attempts by redefining the correction rules. A new metric is designed to effectively identify the corrected location. Numerical results show that the proposed modified BPC decoder achieves a slight improvement in BLER compared with the original BPC, with a dramatic reduction in average complexity. Furthermore, a higher-order version, named MBPC-Ω, is extended to further improve the performance, where the Ω is the maximum correction order. Numerical results show that the higher-order modified BPC achieves a similar BLER performance to existing multiple bit-flipping BP decoders but has around half the latency overhead. In addition, the proposed MBPC-2 decoder performs better than the cyclic redundancy check-aided SCL (CA-SCL) decoder with list size 4 and is slightly worse than the CA-SCL with list size 8 in high signal-to-noise ratio (SNR) regions but with significant decoding latency reduction.