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中国邮电高校学报：英文版

Multiple CRC-aided variable successive cancellation list decoder of polar codes

Miao Cao, Zhao Shuang, Zhao Shengmei

Published Apr 1, 2017• 4 citations
Publisher
DOI
10.1016/s1005-8885(17)60202-4

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Polar coding has found its way into many realms in communications and information theory. In most implementation setups, they are accompanied with the list successive cancellation (LSC) decoding algorithm which is shown to provide a superior error performance compared to the original successive cancellation (SC) decoding method. While the SC decoding is fairly well-studied, the exact math behind LSC's superior performance still remains to be of mystery. Multiple techniques have been proposed to further improve the LSC's error performance or to reduce its computational complexity, which are usually motivated by heuristic reasons and shown through numerical simulations. Most notable example is the CRC-aided LSC, which drastically improves the LSC's performance by concatenating the polar code with some high-rate cyclic redundancy check (CRC) codes.In this paper, we present polar codes that are concatenated with an underlying high-rate convolutional code, which are shown to have superior performances over CRC-aided LSC. We also present a computationally-efficient decoding algorithm for these codes which resembles the techniques used in the Viterbi algorithm, and hence is called the convolutional decoding algorithm. To do this, we revisit the error analysis of the original SC decoding along with the concept of Arıkan's helper genie. We address some shortcomings of the CRC-aided LSC and discuss how to turn around them by emulating a convolutional code instead of a CRC code. Contrary to CRC codes, most of the convolutional codes are not a proper choice for concatenation with polar codes. We introduce the bucketing algorithm to construct suitable punctured convolutional codes for this purpose. The proposed framework can accommodate any such underlying convolutional code, which allows one to search for the optimal convolutional code based on their design parameters.

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Cyclic redundancy check (CRC) assisted list successive cancellation decoding (SCLD) makes polar codes competitive with the state-of-art codes. In this letter, we try to find the optimal CRC for polar codes to further improve its performance. We first analyze the undetected error probability of CRC-aided SCLD as well as the characteristics of Hamming weight distribution of polar codes. Based on these characteristics, a multilevel SCLD-based searching strategy with moderate list size is proposed to compute the minimum Hamming weight distribution (MHWD) of different CRC-concatenated polar codes. Using the searched MHWD, the optimal CRC for polar codes are presented in this letter. Simulation results show that the performance of optimal CRC-aided SCLD significantly outperforms the standard one, especially at high code rate.

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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.

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A complexity-reduced fast successive cancellation list decoder for polar codes

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Polar coding has found its way into many realms in communications and information theory. In most implementation setups, they are accompanied with the list successive cancellation (LSC) decoding algorithm which is shown to provide a superior error performance compared to the original successive cancellation (SC) decoding method. While the SC decoding is fairly well-studied, the exact math behind LSC's superior performance still remains to be of mystery. Multiple techniques have been proposed to further improve the LSC's error performance or to reduce its computational complexity, which are usually motivated by heuristic reasons and shown through numerical simulations. Most notable example is the CRC-aided LSC, which drastically improves the LSC's performance by concatenating the polar code with some high-rate cyclic redundancy check (CRC) codes.In this paper, we present polar codes that are concatenated with an underlying high-rate convolutional code, which are shown to have superior performances over CRC-aided LSC. We also present a computationally-efficient decoding algorithm for these codes which resembles the techniques used in the Viterbi algorithm, and hence is called the convolutional decoding algorithm. To do this, we revisit the error analysis of the original SC decoding along with the concept of Arıkan's helper genie. We address some shortcomings of the CRC-aided LSC and discuss how to turn around them by emulating a convolutional code instead of a CRC code. Contrary to CRC codes, most of the convolutional codes are not a proper choice for concatenation with polar codes. We introduce the bucketing algorithm to construct suitable punctured convolutional codes for this purpose. The proposed framework can accommodate any such underlying convolutional code, which allows one to search for the optimal convolutional code based on their design parameters.
Cyclic redundancy check (CRC) assisted list successive cancellation decoding (SCLD) makes polar codes competitive with the state-of-art codes. In this letter, we try to find the optimal CRC for polar codes to further improve its performance. We first analyze the undetected error probability of CRC-aided SCLD as well as the characteristics of Hamming weight distribution of polar codes. Based on these characteristics, a multilevel SCLD-based searching strategy with moderate list size is proposed to compute the minimum Hamming weight distribution (MHWD) of different CRC-concatenated polar codes. Using the searched MHWD, the optimal CRC for polar codes are presented in this letter. Simulation results show that the performance of optimal CRC-aided SCLD significantly outperforms the standard one, especially at high code rate.
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.