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IEEE International Conference on Computer and Communications (ICCC)

An Improved Segmented Flipped Successive Cancellation List Decoder for Polar Codes

Yunlong Peng, Xingcheng Liu, Jingyun Bao

Published Dec 11, 2020• 4 citations
Publisher

Abstract

Several studies have documented that segmentation can improve the performance of polar codes based on CRC-aided successive cancellation list (CA-SCL) decoding algorithm. In this paper, we propose a new segmented CA-SCL decoder, referred to as improved segmented flipped successive cancellation list (ISF-SCL) decoder, with a reasonable segmentation strategy and a number of extra flipping attempts. Different from the existing methods, in which the uniform segmentation or LLR based segmentation scheme was adopted, a novel segmentation strategy that we firstly analyzed and proposed is based on the distribution of the correct path elimination. Hence, the segment effectiveness is promoted. In addition, to further improve the error correcting performance, a multi-path flipped strategy is proposed to restore the correct path eliminated from the list. Simulation results show that the performance of the ISF-SCL decoding algorithm is superior to the existing segmented CA-SCL decoding algorithms in the low signal-to-noise ratio regime, while the average computational complexity does not increase significantly.

DOI
10.1109/iccc51575.2020.9345126

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Several studies have documented that segmentation can improve the performance of polar codes based on CRC-aided successive cancellation list (CA-SCL) decoding algorithm. In this paper, we propose a new segmented CA-SCL decoder, referred to as improved segmented flipped successive cancellation list (ISF-SCL) decoder, with a reasonable segmentation strategy and a number of extra flipping attempts. Different from the existing methods, in which the uniform segmentation or LLR based segmentation scheme was adopted, a novel segmentation strategy that we firstly analyzed and proposed is based on the distribution of the correct path elimination. Hence, the segment effectiveness is promoted. In addition, to further improve the error correcting performance, a multi-path flipped strategy is proposed to restore the correct path eliminated from the list. Simulation results show that the performance of the ISF-SCL decoding algorithm is superior to the existing segmented CA-SCL decoding algorithms in the low signal-to-noise ratio regime, while the average computational complexity does not increase significantly.
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.
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.
Existing studies have documented that flipping operation can improve the performance of polar codes based on CRC-aided successive cancellation list (CA-SCL) decoding algorithm. However, the introduction of the flips greatly increases the complexity and delay of the decoder as well. In this paper, we analyzed the error distribution in the CA-SCL decoding and proposed a new efficient flipping set, key set, to reduce the complexity of the SCL-Flip decoding by narrowing down the size of the flipping set applicable. Different from the critical set which focuses on rate-1 nodes only, the key set can be constructed dynamically based on the results of the original CA-SCL decoding. In addition, we proposed an order-1 SCL-Flip decoder based on the key set to reduce the decoding complexity. Simulation results showed that the key set has a high accuracy of locating the first error and our proposed algorithm has almost no performance degradation compared with the existing SCL-Flip algorithms while the average complexity is reduced significantly.
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.
A successive cancellation list (SCL) decoder with the assistance of a cyclic redundancy check (CRC) can provide competitive decoding performance for polar codes compared with the state-of-the-art codes. In this paper, we adopt a bit-flip algorithm for the CRC-assisted SCL decoder to further improve the error-correcting performance. We first introduce a new bit-flip criterion for the SCL decoder. To support this criterion, we give the metric to identify the positions that need to be flipped. To verify the superiority of the proposed bit-flip criterion, we also consider a kind of SCL-flip decoder whose criterion is very similar with the existing one and we will prove that its performance is worse than the decoder with the proposed bit-flip criterion. The simulation results show that the decoder with the proposed bit-flip criterion outperforms both the standard CRC-assisted SCL decoder and the existing SCL-based bit-flip decoder.
An improved CA-SCL (CRC-Aided Successive Cancellation List) decoding algorithm for Polar codes is proposed in this paper. By introducing the global cyclic redundancy check and local parity check, a lower bit error rate is obtained comparing with the known results. The new algorithm constructs a prune decoding path by the parity check in the local processing. Since the parity check can only detect an odd number of errors, the global CRC is used to increase the error detection ability and the decoding accuracy. The performance of the improved decoding algorithm is better than the known results, especially when the code length is either less than or equal to 512, and the code rate is not greater than 0.5 in case of the signal-to-noise ratio (SNR) higher than 3dB. In particular, when the code length is 256 with code rate of 0.5 and decoding list size of 32 under the condition of bit error rate 10-5on the AWGN channel, the proposed algorithm has around 0.25dB and 0.55dB performance gain comparing with that of the CA-SCL and SCL algorithms, respectively.