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International Conference on Wireless Communications and Signal Processing (WCSP)

An Improved Multiple Bit-Flipping Successive Cancellation Decoding Algorithm for Polar Codes

Sha Sha, Li Guo Zhang, Yejun He

Published Oct 21, 2020• 1 citation
Publisher

Abstract

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.

DOI
10.1109/wcsp49889.2020.9299883

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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.
Polar codes, as the coding scheme for the control channel in fifth-generation mobile communication technology (5G), have attracted widespread attention since their proposal. As a mainstream decoding algorithm for polar codes, the successive cancellation list (SCL) decoder usually improves the error correction performance by increasing the list size, but this method suffers from the problems of high decoding complexity. To address this problem, this paper proposes a layered-search bit-flipping (LS-SCLF) decoding algorithm based on SCL decoding. Firstly, a new flip-bit metric is proposed, which derives a formula to approximate the probability of an error occurring in an information bit. This formula introduces a perturbation parameter to improve the calculation accuracy. Secondly, a compromise scheme for determining the perturbation parameter is proposed. The scheme uses Monte Carlo simulation to determine an optimized parameter for the precise positioning of the first erroneous decoded bit under different decoding conditions. Finally, a layered search strategy is adopted to sequentially search the erroneous decoded bits from the low order to high order, which can correct up to multiple bits at the same time. Simulation results show that the proposed algorithm achieves improved error correction performance with a slight increase in decoding complexity compared to the generalized SCL-Flip (GSCLF) decoding algorithm. This algorithm also achieves a good balance between the error correction performance and decoding complexity.
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 have garnered significant attention since they were proposed due to their capacity-achieving properties and their low-complexity decoding process, and they were selected as the coding scheme for the control channel in 5G mobile communication technology. A successive cancellation list (SCL) decoder, aided by a cyclic redundancy check (CRC), performs the competitive error correcting performance for polar codes compared to other sophisticated codes. The SCL-Flip decoding algorithm is proposed to enhance the error correction performance of the SCL. However, the SCL-Flip is hampered by a high decoding complexity due to the necessary selection and sorting process of path metrics (PMs). Additionally, it requires a large number of iterations to achieve a good error correction performance. In this paper, we propose the error segment bit-flip (ES-SCL-Flip) decoding algorithm, a simplified bit-flip approach for the SCL decoder based on analyzing the distributions of the first error bit. Firstly, we construct an index set with a high probability of the first erroneous bit. Second, a bit-flip criterion is introduced to prevent the costly operation of the PM selection and sorting without compromising the error correction performance. Finally, a search strategy is employed that utilizes segmented error indication to target and rectify the initial error segment sequentially. The simulation results demonstrate that the ES-SCL-Flip decoder provides an improved error correction performance with only a minimal increase in decoding complexity compared to the conventional CRC-aided SCL decoder. This algorithm attains a commendable equilibrium between the error correction performance and decoding complexity.
Polar codes have attracted significant attention in the field of communication, for the capacity-achieving under binary-input discrete memoryless channels (BDMCs). On the basis of successive cancellation (SC) decoding algorithm, many excellent methods have been developed to improve the decoding performance on short and medium codes. In this paper, an LLR-based segmented flipped successive cancellation list (LLR-based SF-SCL) decoding algorithm is proposed, where the information bits are divided into segments for early bit-flipping and termination. In order to make the unreliable bits evenly distributed in each sub-block, an LLR-based segmentation scheme is applied. Simulation results show that the proposed segmented flipped algorithm is superior to CRC-aided successive cancellation list (CA-SCL) algorithm in the block error rate (BLER) performance, and LLR-based segmentation scheme has better performance compared to uniform segmentation scheme.
Successive cancellation (SC) decoding of polar codes may bring about error propagation that needs to be mitigated. In this paper, we present a new SC Flipping (SCFlip) decoder, named bit error rate (BER) evaluation based SCFlip (BER-SCFlip), which can accurately target the first error bit and correct it with a high probability. Thus, a high error correction capability and a low decoding complexity can be achieved. First, we propose a new criterion to find out the most suspicious error bit. Those non-frozen bits that have higher decoding BERs derived from log-likelihood-ratios (LLRs) after SC decoding than the corresponding expected ones estimated via Gaussian Approximation (GA), are collected into the flip-bits set. These candidate bits will be flipped one by one according to their SC decoding orderings in extra decoding attempts until the decoded codeword passes cyclic redundancy check (CRC) or a predetermined maximum number of extra attempts is reached. We then propose an extended version of BER-SCFlip, named BER-SCFlip-w with the capability to correct up to w error bits in each extra decoding attempt. By combining our criterion for the flip-bits selection with that of Dynamic SCFlip (D-SCFlip), the proposed BER-SCFlip-w significantly reduces decoding complexity and latency while maintaining the superior error-correction performance close to that of D-SCFlip-w. The simulation results show that the proposed schemes are competitive among existing SCFlip algorithms and could achieve the error-correction performance approaching that of CRC-aided SCL decoding under list size L = 16 while maintaining low complexity.
Successive cancellation list (SCL) decoding for polar codes has the ability to achieve Shannon capacity over the binary discrete memoryless channel. However, a large list size is required to achieve the Shannon capacity limit. Consequently, this paper proposes a novel iterative method for the CA-SCL decoder based on frozen bits to improve the error-correction performance of CA-SCL decoding for polar codes with smaller list sizes. The proposed technique determines the vulnerable channel log-likelihood ratios (LLRs) for frozen bits that degrade the CA-SCL decoding error correction performance and corrects them for the next CA-SCL decoding attempt. We analyze the behavior of wrongly estimated LLRs of frozen bits during CA-SCL decoding and design an attenuation factor set using a greedy algorithm. The proposed technique employs iterative CA-SCL decoding and revises the wrongly estimated frozen bit LLRs using the attenuation factor set during the decoding process. The simulation results show that the proposed technique achieves a block error rate (BLER) performance gain of up to 0.25 compared with the CA-SCL decoder, with a minor increase in computational complexity. Moreover, the attenuation factor set can be adjusted arbitrarily to balance performance and complexity.