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Journal of the Korea Society of Digital Industry and Information Management

Enhanced Belief Propagation Polar Decoder for Finite Lengths

Shajeel Iqbal, GoangSeog Choi

Published Sep 30, 2015• 0 citations
Publisher

Abstract

In this paper, we discuss the belief propagation decoding algorithm for polar codes. The performance of Polar codes for shorter lengths is not satisfactory. Motivated by this, we propose a novel technique to improve its performance at short lengths. We showed that the probability of messages passed along the factor graph of polar codes, can be increased by multiplying the current message of nodes with their previous message. This is like a feedback path in which the present signal is updated by multiplying with its previous signal. Thus the experimental results show that performance of belief propagation polar decoder can be improved using this proposed technique. Simulation results in binary-input additive white Gaussian noise channel (BI-AWGNC) show that the proposed belief propagation polar decoder can provide significant gain of 2 dB over the original belief propagation polar decoder with code rate 0.5 and code length 128 at the bit error rate (BER) of $10^{-4}$ .

DOI
10.17662/ksdim.2015.11.3.045

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In this paper, we discuss the belief propagation decoding algorithm for polar codes. The performance of Polar codes for shorter lengths is not satisfactory. Motivated by this, we propose a novel technique to improve its performance at short lengths. We showed that the probability of messages passed along the factor graph of polar codes, can be increased by multiplying the current message of nodes with their previous message. This is like a feedback path in which the present signal is updated by multiplying with its previous signal. Thus the experimental results show that performance of belief propagation polar decoder can be improved using this proposed technique. Simulation results in binary-input additive white Gaussian noise channel (BI-AWGNC) show that the proposed belief propagation polar decoder can provide significant gain of 2 dB over the original belief propagation polar decoder with code rate 0.5 and code length 128 at the bit error rate (BER) of 10−410^{-4}10−4 .
Abstract In this letter, a modified message passing algorithm to prevent short cycles in the factor graph is proposed and combined with a relaxation technique to improve the performance of cyclic redundancy check aided belief propagation decoding for polar codes. Numerical results show that the proposed scheme can achieve a 0.7 dB coding gain, for the code rate of 0.5 at the block error rate of 10 −5 with a comparable average number of iterations over the pure belief propagation decoding scheme when the code block length is 1024.
Polar codes have become the channel coding scheme for control channel of enhanced mobile broadband in the 5G communication systems. Belief propagation (BP) decoding of polar codes has advantages of low decoding latency and high parallelism but achieves worse bit error ratio (BER) performance compared with the successive cancellation list (SCL) decoding scheme. In this paper, an improved BP list (IBPL) decoding algorithm is proposed with comparable BER performance to SCL algoritm. Firstly, the optimal permuted factor graph is analyzed for polar codes, which improves the performance of the BP decoder without path extension. Furthermore, based on the optimal graph, the bit metric and decoding path metric are proposed to extend and prune the decoding path. The proposed IBPL decoder is focused on not only the permutation of polar codes but also the reliabilities of decoded codewords during each iteration of BP decoding, which has a more accurate decoding path list. The simulation results show that the proposed IBPL decoder improves the BER performance compared with the original BP decoder significantly, and can approach the performance of the SCL decoder at low signal to noise ratio regions.
Polar codes have been recently proposed as the first low complexity class of codes that can provably achieve the capacity of symmetric binary-input memoryless channels. Here, we study the bit error rate performance of finite-length polar codes under Belief Propagation (BP) decoding. We analyze the stopping sets of polar codes and the size of the minimal stopping set, called “stopping distance”. Stopping sets, as they contribute to the decoding failure, play an important role in bit error rate and error floor performance of the code. We show that the stopping distance for binary polar codes, if carefully designed, grows as O(√N) where N is the code-length. We provide bit error rate (BER) simulations for polar codes over binary erasure and gaussian channels, showing no sign of error floor down to the BERs of 10-11. Our simulations asserts that while finite-length polar codes do not perform as good as LDPC codes in terms of bit error rate, they show superior error floor performance. Motivated by good error floor performance, we introduce a modified version of BP decoding employing a guessing algorithm to improve the BER performance of polar codes. Our simulations for this guessing algorithm show two orders of magnitude improvement over simple BP decoding for the binary erasure channel (BEC), and up to 0.3 dB improvement for the gaussian channel at BERs of 10-6.
Short block-length polar-like codes showcase exceptional error correction performance (ECP) using sequential decoding or successive cancellation list decoding with a large list size. However, achieving a high level of reliability with these methods involves high-latency decoding. To meet the growing demand for low-latency communication with acceptable complexity, belief propagation (BP) decoding emerges as an attractive option, although its ECP is known to fall short of those high-latency alternatives. In this paper, we propose an enhanced BP decoding approach for polar codes, leveraging reinforcement learning (RL) to optimize the message-passing schedule. Moreover, we investigate the design of the polar code rate profile and corresponding Tanner graph representation to enhance the benefits of RL. Numerical results demonstrate a performance gain of more than 1 dB for polar codes with a length of 128 and a rate of 0.5 compared to conventional BP decoding alone at highEb/N0values, demonstrating the promise of the proposed approach.
A polar code decoder based on the belief propagation algorithm is desirable because of the potentially low latency and its suitability for parallel execution on multicore and SIMD processors. However, current state-of-the-art algorithms require many iterations to achieve comparable bit and frame error rate compared to successive cancellation algorithms. Also, the current state-of-the-art belief propagation algorithms have a high computational complexity compared to successive cancellation. In this paper we present an enhanced belief propagation algorithm, in which parts of the computations are altered to reduce the negative effect of the short cycles in the polar code factor graph. Our proposed algorithm has a gain of approx+0.4mathbf{dB} in both frame and bit error rate compared to successive cancellation and a gain of approx+0.16mathbf{dB} and approx+0.13mathbf{dB} at a frame and bit error rate of 10-3 respectively, compared to belief propagation. Also, the maximum number of iterations of our algorithm is reduce to 0.6cdot I_{max}. As a result, the latency is up to approx 11 times lower compared to successive cancellation and up to approx 1.8 times lower compared to the current state-of-the-art belief propagation polar code algorithm. Furthermore, the reduction in the maximum iteration count results in a lower power consumption after implementation.
Belief Propagation(BP) decoders of Polar Codes can run in parallel and have a remarkable throughput achievement at a cost of performance degradation, when compared with other decoding algorithms of polar codes. The existing improved algorithms still have a gap to be optimized in performance, complexity or latency. This paper proposes a modified BP flipping algorithm by introducing random penalty items into the reliability metrics of bits to correct un-converged errors under the type of noise with Gaussian distributions considered. Simulation results illustrate that the proposed penalizing method can exhibit significant performance gains over the original BP and other three existing BP flipping decoding algorithms with different blocks in the additive white Gaussian noise channel(AWGN) under a lower decoding latency. This shows the proposed scheme identifies the error-prone bits more efficiently.