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Globecom

Generalized SCL-Flip Decoding of Polar Codes

Yaoxin Pan, Chung-Hsuan Wang, Yeong-Luh Ueng

Published Dec 1, 2020• 18 citations
Publisher

Abstract

In this paper, two improvements for successive cancellation list flip (SCL-Flip) decoding are presented for polar codes. First, a novel bit-selection metric based on path metric (PM) is introduced. With the proposed metric, the improved scheme can have lower complexity and saturate faster than other state-of-the-art decoders. Second, we generalize the SCL-Flip decoding, denoted SCL-Flip-ω, to flip the decision in path competition at most ω times in decoding process. We analyze the frequency of channel-induced error under various circumstances, measure the trade-off between error-correction performance and complexity, and then propose SCL-Flip-2 decoding which is the first SCL-based decoding that allows for multiple bits for flipping to the best of our knowledge. Simulation results reveal that the proposed decoding with a small list size can achieve a better performance than CA-SCL decoding with a large list size while keeping the complexity low.

DOI
10.1109/globecom42002.2020.9321982

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Recently, a generalized successive cancellation list (SCL) decoder implemented with shifted-pruning (SP) scheme, namely the SCL-SP-ω decoder, is presented for polar codes, which is able to shift the pruning window at most ω times during each SCL re-decoding attempt to prevent the correct path from being eliminated. The candidate positions for applying the SP scheme are selected by a shifting metric based on the probability that the elimination occurs. However, the number of exponential/logarithm operations involved in the SCL-SP-ω decoder grows linearly with the number of information bits and list size, which leads to high computational complexity. In this paper, we present a detailed analysis of the SCL-SP-ω decoder in terms of the decoding performance and complexity, which unveils that the choice of the shifting metric is essential for improving the decoding performance and reducing the re-decoding attempts simultaneously. Then, we introduce a simplified metric derived from the path metric (PM) domain, and a custom-tailored deep learning (DL) network is further designed to enhance the efficiency of the proposed simplified metric. The proposed metrics are both free of transcendental functions and hence, are more hardware-friendly than the existing metrics. Simulation results show that the proposed DL-aided metric provides the best error correction performance as comparison with the state of the art.

China Communications•Jan 1, 2023•13 citations
In this paper, two improvements for successive cancellation list flip (SCL-Flip) decoding are presented for polar codes. First, a novel bit-selection metric based on path metric (PM) is introduced. With the proposed metric, the improved scheme can have lower complexity and saturate faster than other state-of-the-art decoders. Second, we generalize the SCL-Flip decoding, denoted SCL-Flip-ω, to flip the decision in path competition at most ω times in decoding process. We analyze the frequency of channel-induced error under various circumstances, measure the trade-off between error-correction performance and complexity, and then propose SCL-Flip-2 decoding which is the first SCL-based decoding that allows for multiple bits for flipping to the best of our knowledge. Simulation results reveal that the proposed decoding with a small list size can achieve a better performance than CA-SCL decoding with a large list size while keeping the complexity low.
In this paper, an improvement for SC list flip (SCL-Flip) decoding is presented for polar codes. A novel bit-selection metric for critical set (set of information symbols of polar codes being flipped during additional decoding attempts) based on path metric of successive cancellation list (SCL) decoding is suggested. With the proposed metric, the improved SCL scheme based on special nodes (SN) decoders was developed. This decoder will be denoted by GSCLF. The main idea of the proposed decoder is joint using of two approaches: first one is a fast decoding of special nodes in binary tree representation of polar code (e.g., some special nodes in tree representation of polar code that allow efficient list decoding with low complexity) and the second one is an applying of additional decoding attempts (flips) in the case when initial decoding was erroneous. The simultaneous use of these two approaches results in both a significant reduction in spatial complexity and a significant reduction in the number of computations required for decoding whereas keeping excellent performance. Simulation results presented in this paper allow us to conclude that the computational complexity of the proposed GSCLF decoder is from 66% to 80% smaller than the one of SCL-32 decoder.
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, 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.
Successive cancellation (SC) decoding algorithm and successive cancellation list (SCL) decoding algorithm are two common decoding methods for polar codes. The SC decoding algorithm has low complexity, but in its decoding process, the bits with small channel indices are used to assist the decoding of the bits with large channel indices. Therefore, the bit being decoded depends on the bits that have already been decoded which causes error propagation. On the basis of SC decoding, the SCL decoding algorithm overcomes the problem of error propagation by widening the path search width and retaining multiple paths at the same time in the decoding process. However, the complexity of SCL decoding is higher than that of SC decoding. Without changing the performance of the SCL decoding algorithm, we propose a low-complexity SCL decoding algorithm based on path metric (PM). After the last frozen bit is decoded, the path with the smallest PM is selected, and the subsequent nodes adopt SC decoding. Through this combination of SCL decoding and SC decoding, the complexity of the SCL decoding algorithm can be effectively reduced while the SCL decoding performance remains unchanged, especially in the case of high code rates.
The eBCH-polar codes is a powerful way to construct polar codes. With high minimum Hamming distance, it outperforms ordinary Polar codes under successive cancellation list (SCL) decoder. However, the absence of cyclic redundancy check (CRC) bits in eBCH-polar codes makes it challenging to adopt SCL-flip (SCLF) decoding scheme. In this research, we propose a flip scheme activated by a Normalized Path Metric (PM) range and a mismatch criterion, which respectively leverage the properties of SCL decoding and dynamic frozen bits of eBCH-polar codes. This work also improves the selection the flipping bits by modifying metric to account for the structure of dynamic frozen bits and reduce the search space. Based on these modifications, we proposed SCLF-1 and SCLF-2 decoding algorithms for eBCH-polar codes. Simulation results show that both of the proposed decoding schemes achieve superior performance compared to other contemporary decoding algorithms for CRC aided polar (CA-polar) codes, demonstrating enhanced error rates performance within the same decoding attempt.
Recently, a generalized successive cancellation list (SCL) decoder implemented with shifted-pruning (SP) scheme, namely the SCL-SP-ω decoder, is presented for polar codes, which is able to shift the pruning window at most ω times during each SCL re-decoding attempt to prevent the correct path from being eliminated. The candidate positions for applying the SP scheme are selected by a shifting metric based on the probability that the elimination occurs. However, the number of exponential/logarithm operations involved in the SCL-SP-ω decoder grows linearly with the number of information bits and list size, which leads to high computational complexity. In this paper, we present a detailed analysis of the SCL-SP-ω decoder in terms of the decoding performance and complexity, which unveils that the choice of the shifting metric is essential for improving the decoding performance and reducing the re-decoding attempts simultaneously. Then, we introduce a simplified metric derived from the path metric (PM) domain, and a custom-tailored deep learning (DL) network is further designed to enhance the efficiency of the proposed simplified metric. The proposed metrics are both free of transcendental functions and hence, are more hardware-friendly than the existing metrics. Simulation results show that the proposed DL-aided metric provides the best error correction performance as comparison with the state of the art.