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Entropy

Reinforcement Learning for Bit-Flipping Decoding of Polar Codes

Xiumin Wang, Jinlong He, Jun Li, Liang Shan

Published Jan 30, 2021• 4 citations
Publisher

Abstract

A traditional successive cancellation (SC) decoding algorithm produces error propagation in the decoding process. In order to improve the SC decoding performance, it is important to solve the error propagation. In this paper, we propose a new algorithm combining reinforcement learning and SC flip (SCF) decoding of polar codes, which is called a Q-learning-assisted SCF (QLSCF) decoding algorithm. The proposed QLSCF decoding algorithm uses reinforcement learning technology to select candidate bits for the SC flipping decoding. We establish a reinforcement learning model for selecting candidate bits, and the agent selects candidate bits to decode the information sequence. In our scheme, the decoding delay caused by the metric ordering can be removed during the decoding process. Simulation results demonstrate that the decoding delay of the proposed algorithm is reduced compared with the SCF decoding algorithm, based on critical set without loss of performance.

DOI
10.3390/e23020171

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A traditional successive cancellation (SC) decoding algorithm produces error propagation in the decoding process. In order to improve the SC decoding performance, it is important to solve the error propagation. In this paper, we propose a new algorithm combining reinforcement learning and SC flip (SCF) decoding of polar codes, which is called a Q-learning-assisted SCF (QLSCF) decoding algorithm. The proposed QLSCF decoding algorithm uses reinforcement learning technology to select candidate bits for the SC flipping decoding. We establish a reinforcement learning model for selecting candidate bits, and the agent selects candidate bits to decode the information sequence. In our scheme, the decoding delay caused by the metric ordering can be removed during the decoding process. Simulation results demonstrate that the decoding delay of the proposed algorithm is reduced compared with the SCF decoding algorithm, based on critical set without loss of performance.
The flip-successive cancellation (SCF) decoding algorithm is a decoding scheme to improve the performance of the SC decoding algorithm under short code length by flipping erroneous bits in initial SC decoding. The degraded performance of the SCF decoding algorithm is usually caused by the wrong locating of the first erroneous bit or additional erroneous bits. To address this issue, we propose a machine learning based multi-flips SC decoding scheme (ML-MSCF), which can improve the performance of the SCF decoding algorithm with multiple flips based on the long short-term memory (LSTM) network and reinforcement learning (RL). Specifically, we use a LSTM network to locate the first erroneous bit when initial SC decoding fails, then the outputs of the LSTM network are used as the action space of RL to identify additional erroneous bits in the followed procedure. Simulation results show that the proposed scheme can achieve performance improvement of 0.2-0.3dB over the stateof-art SCF decoding algorithm on both the bit error ratio (BER) and the frame error rate (FER) with less decoding latency.
In this paper, we introduce a novel bit-flipping algorithm for fast successive cancellation (FSC) decoding of polar codes. In particular, we first propose a new bit-flipping strategy tailored to single parity-check (SPC) constituent codes of polar codes. A parameterized bit-flipping model is then developed and reinforcement learning (RL) is used to optimize the parameters. Our experimental results show that for a polar code of length 512 with 256 information bits, the proposed decoder has a better or similar error-correction performance compared to the state-of-the-art fast DSCF (FDSCF) decoding algorithm when the same number of maximum decoding attempts is considered.
Bit flipping was first used to improve the decoding performance of successive cancellation (SC) decoder. Since SC decoding process is serial, so the first bit that goes wrong in the decoding process will cause several subsequent bits to go wrong, which will suffer from higher decoding delay than belief propagation (BP) parallel decoding. In order to meet the performance of 5G low latency and high reliability, BP decoding algorithm have received a lot of attention. However, at medium and high signal-to-noise ratios (SNR), BP decoding does not perform as well as the SC list (SCL) decoding algorithm. Hence, BP decoding algorithm borrows bit-flip strategies from SC bit flip (SCF) decoder to improve the performance. The performance of BP bit flip (BPF) decoding depends on whether the construction of the flip set is correct, so this letter proposes a flip set construction approach based on the standard deviation of the log-likelihood ratio (LLR) and the reliability weight of polarized channels, which is comparable to the existing BPF decoding, the improved algorithm can identify the error-prone bits more efficiently and improve the decoding performance.
Polar codes is the only coding scheme in the world that has been proved that the Shannon threshold is reachable. Because of the high time delay caused by the serial characteristic of Successive Cancellation (SC) decoding, the Belief Propagation (BP) decoding has received more attention because of its higher throughput. However, because its decoding performance is not as good as SC decoding, Bit-Flip (BF) decoding is used in BP. Aiming at the inaccurate construction of flip set in current bit flipping decoding, this paper proposes a new bit error rate BP BF (BPF) decoding algorithm, which is used to construct flip set. We also propose rough flip set and fine flip set Concept of flip set. The rough flip set is constructed by the variance of the characteristics of data stability. The range of the flip set is reduced by the difference in bit error rate, that is, the fine flip set. The research results show that the algorithm proposed in this paper is superior to the current best decoding algorithms such as BP, Enhanced BPF (EBPF) and Log Likelihood Ratio BPF (BPF-LLR). At the same time, the number of iterations of the algorithm is significantly reduced compared with other bit-flipping decoding algorithms.
The key to successive cancellation (SC) flip decoding of polar codes is to accurately identify the first error bit. The optimal flipping strategy is considered difficult due to lack of an analytical solution. Alternatively, we propose a deep learning aided SC flip algorithm. Specifically, before each SC decoding attempt, a long short-term memory (LSTM) network is exploited to either (i) locate the first error bit, or (ii) undo a previous "wrong" flip. In each SC attempt, the sequence of log likelihood ratios (LLRs) derived in the previous SC attempt is exploited to decide which action to take. Accordingly, a two-stage training method of the LSTM network is proposed, i.e., learn to locate first error bits in the first stage, and then to undo "wrong" flips in the second stage. Simulation results show that the proposed approach identifies error bits more accurately and achieves better block error rate performance than the state-of-the-art SC flip algorithms.
Although original successive cancellation flip (SCF) decoding of the polar codes can identify the first error position and flip the error, decoding still fails when other errors occur after the corrected error bit. Therefore, the improvement of the block error rate (BLER) performance is limited. In this paper, we present an improved algorithm that can correct multiple error bits, named as improved multiple bit-flipping successive cancellation decoding algorithm. First, multiple sets are constructed by calculating the log likelihood ratio (LLR) of each information bit. Then, a bit is selected and corrected from the first set when original decoding fails; two bits are selected and flipped from the second set when all bits in the first set cannot be successfully decoded; when all bits combinations in the second set are flipped but the output vector still does not match the input vector, three bits are selected and corrected from the third set. Simulation results show that the BLER performance of the improved algorithm is better than that of the successive cancellation list decoding (SCL) decoding algorithm with a list size of L = 8 for N = 256. When N = 1024 and SNR = 3 dB, the BLER performance of improved algorithm is slightly better than that of SCL decoding algorithm with a list size of L = 4.