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International Symposium on Networks, Computers and Communications (ISNCC)

An Improved CA-SCL Decoding Algorithm for Polar Code

Yunfei Tai, Kezhen Li, Liang Zhou, Shu Liu, Xilin Zhang

Published Jul 19, 2022• 3 citations
Publisher

Abstract

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.

DOI
10.1109/isncc55209.2022.9851768

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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.
Cyclic redundancy check (CRC)-aided successive cancellation list (CA-SCL) decoding algorithm has brought good error performance. Recently, some researchers utilized multiple CRC codes to reduce decoding complexity of CA-SCL decoding algorithm. However, based on CA-SCL decoding frame, we not only reduce decoding complexity but also improve error performance. We divide polar codeword into independent sub-blocks during the process of encoding. Meanwhile, locations of multiple CRC are optimized according to a value of each average Bhattacharyya parameter. Finally, for CA-SCL decoding, results indicate that our constructed polar codes show an admirable error performance and low decoding complexity than that of equal sub-block codewords.
In order to make a better trade-off between computational complexity and decoding performance, a cyclic redundancy check (CRC)-aided split-reduced successive cancellation list (CA-SR-SCL) algorithm is proposed in this paper. Based on the splitting rule defined in split-reduced SCL (SR-SCL) algorithm and enhanced-SR-SCL (ESR-SCL) algorithm, the splitting characteristics of the correct decoding path are calculated. In addition, a new pruning rule is proposed to timely delete the candidate paths that split frequently, and a CRC detector is appended to improve the error correction performance. Compared to the ESR-SCL algorithm, simulation results demonstrate that the proposed algorithm can achieve better performance with lower computational complexity.
Novel successive cancellation list (SCL) decoding schemes of Polar codes by exploiting the error correction (EC) capability of the cyclic redundancy check (CRC) codes are proposed in this paper. Different from the schemes in the literature that only considered the error detection capability of CRC, the proposed schemes aim to improve the performance of CRC-aided Polar decoding to the most by benefiting from the potential EC capability of CRC. Specifically, we first propose a basic decoding scheme, named CRC error-correction-aided successive cancellation list (CRC-EC-SCL) decoding, by introducing the look-up-table-based CRC EC method into the Polar SCL decoding process. Then, based on the basic scheme, we further propose the segmented-CRC-EC-SCL decoding scheme. By segmented-CRC, the information block is divided into multiple segments and each segment is attached with a shorter CRC sequence. By conducting the CRC-EC-aided coding for each of the segments, multiple erroneous bits can be corrected early and error propagation can, thus, be efficiently suppressed. The simulation results show that both of the proposed decoding schemes have a significant performance gain over the classic CRC-EC-SCL decoding scheme. Especially for the segmented-CRC-EC-SCL, the performance gain at a frame error rate of 10−4is about 0.4 dB. Moreover, the average computation complexity of the segmented-CRC-EC-SCL is close to the classic scheme.
Due to the unsatisfactory block error rate (BLER) performance of short or moderate block , the further development of polar codes is limited. In this paper, the parity-check codes concatenated cyclic redundancy check aided successive cancellation list (CA-SCL) decoding algorithms are studied. Then, an efficient concatenated method, double-parity-check CA-SCL (DP-CA-SCL) polar codes, is proposed according to exiting parity-check decoding algorithms. Not only can this new method improve the BLER performance in short or moderate block, but also it can guarantee the reduction of complexity relative to original CA-SCL method. The simulations in additive white Gaussian noise channel with binary phase shift keying modulation reveal that the DP-CA-SCL polar codes can provide significant performance gains. Comparing to the original CA-SCL decoding, there are 0.5 dB performance gains using proposed method at BLER of 10-3with (128, 64) polar codes. For another moderate block (256, 128) polar codes, it can also guarantee performance gains at least 0.18 dB.
As an indispensable part of cyclic redundancy check aided Successive Cancellation List (CA-SCL) decoding and SCL bit flipping (CA-SCLF) decoding, sort operation increases the complexity of decoding.In order to minimize the quantity of sorting and simplify the complexity of SCLF decoding algorithm, this paper proposes an improved SCLF decoding algorithm, called NSCLF algorithm, which reduces the number of paths involved in sorting by detecting and pruning paths whose bit metric value is less than the set threshold before sorting operations.Meanwhile, pruning paths are dynamically selected according to node states during the flipping process.The flipping path selections are more accurate and the number of flipping correspondingly decreases.The simulation results demonstrate that when SNR is 3dB, the code length and code rate , while maintaining decoding performance comparable to that of traditional CA-SCLF, the sorting operation of our proposed NSCLF is about 93% less than that of traditional CA-SCLF, and the decoding complexity is less than that of traditional CA-SCLF.
In this letter, three post-processing schemes for cyclic redundancy check (CRC-)aided successive cancellation list (CA-SCL) decoding are presented for polar codes. The re-decoding based on our post-processing schemes can effectively alleviate both the channel and decision errors encountered via CA-SCL decoding. Simulation results show that our schemes perform better than conventional re-decoding schemes and can be incorporated into a polar decoder that has a small list size to achieve a performance that is expected for a large list size.