Research on encoding and decoding of non-binary polar codes over GF(2m)
Binary Polar Codes (BPCs) have advantages of high-efficiency and capacity-achieving but suffer from large latency due to the Successive-Cancellation List (SCL) decoding. Non-Binary Polar Codes (NBPCs) have been investigated to obtain the performance gains and reduce latency under the implementation...
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| Format: | Article |
| Language: | English |
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KeAi Communications Co., Ltd.
2022-06-01
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| Series: | Digital Communications and Networks |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2352864822000050 |
| _version_ | 1811241581258211328 |
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| author | Shufeng Li Mingyu Cai Robert Edwards Yao Sun Libiao Jin |
| author_facet | Shufeng Li Mingyu Cai Robert Edwards Yao Sun Libiao Jin |
| author_sort | Shufeng Li |
| collection | DOAJ |
| description | Binary Polar Codes (BPCs) have advantages of high-efficiency and capacity-achieving but suffer from large latency due to the Successive-Cancellation List (SCL) decoding. Non-Binary Polar Codes (NBPCs) have been investigated to obtain the performance gains and reduce latency under the implementation of parallel architectures for multi-bit decoding. However, most of the existing works only focus on the Reed-Solomon matrix-based NBPCs and the probability domain-based non-binary polar decoding, which lack flexible structure and have a large computation amount in the decoding process, while little attention has been paid to general non-binary kernel-based NBPCs and Log-Likelihood Ratio (LLR) based decoding methods. In this paper, we consider a scheme of NBPCs with a general structure over GF(2m). Specifically, we pursue a detailed Monte-Carlo simulation implementation to determine the construction for proposed NBPCs. For non-binary polar decoding, an SCL decoding based on LLRs is proposed for NBPCs, which can be implemented with non-binary kernels of arbitrary size. Moreover, we propose a Perfect Polarization-Based SCL (PPB-SCL) algorithm based on LLRs to reduce decoding complexity by deriving a new update function of path metric for NBPCs and eliminating the path splitting process at perfect polarized (i.e., highly reliable) positions. Simulation results show that the bit error rate of the proposed NBPCs significantly outperforms that of BPCs. In addition, the proposed PPB-SCL decoding obtains about a 40% complexity reduction of SCL decoding for NBPCs. |
| first_indexed | 2024-04-12T13:38:18Z |
| format | Article |
| id | doaj.art-6860222bebaf43d5a90e5f84b73f0342 |
| institution | Directory Open Access Journal |
| issn | 2352-8648 |
| language | English |
| last_indexed | 2024-04-12T13:38:18Z |
| publishDate | 2022-06-01 |
| publisher | KeAi Communications Co., Ltd. |
| record_format | Article |
| series | Digital Communications and Networks |
| spelling | doaj.art-6860222bebaf43d5a90e5f84b73f03422022-12-22T03:30:55ZengKeAi Communications Co., Ltd.Digital Communications and Networks2352-86482022-06-0183359372Research on encoding and decoding of non-binary polar codes over GF(2m)Shufeng Li0Mingyu Cai1Robert Edwards2Yao Sun3Libiao Jin4The State Key Laboratory of Media Convergence and Communication, School of Information and Engineering, Communication University of China, Beijing, 100024, China; Corresponding author.The State Key Laboratory of Media Convergence and Communication, School of Information and Engineering, Communication University of China, Beijing, 100024, ChinaThe Wolfson School of Mechanical Electrical and Manufacturing Engineering, Loughborough University, Leicestershire, LE11 3TE, UKJames Watt School of Engineering, University of Glasgow, G12 8QQ, Scotland, UKThe State Key Laboratory of Media Convergence and Communication, School of Information and Engineering, Communication University of China, Beijing, 100024, ChinaBinary Polar Codes (BPCs) have advantages of high-efficiency and capacity-achieving but suffer from large latency due to the Successive-Cancellation List (SCL) decoding. Non-Binary Polar Codes (NBPCs) have been investigated to obtain the performance gains and reduce latency under the implementation of parallel architectures for multi-bit decoding. However, most of the existing works only focus on the Reed-Solomon matrix-based NBPCs and the probability domain-based non-binary polar decoding, which lack flexible structure and have a large computation amount in the decoding process, while little attention has been paid to general non-binary kernel-based NBPCs and Log-Likelihood Ratio (LLR) based decoding methods. In this paper, we consider a scheme of NBPCs with a general structure over GF(2m). Specifically, we pursue a detailed Monte-Carlo simulation implementation to determine the construction for proposed NBPCs. For non-binary polar decoding, an SCL decoding based on LLRs is proposed for NBPCs, which can be implemented with non-binary kernels of arbitrary size. Moreover, we propose a Perfect Polarization-Based SCL (PPB-SCL) algorithm based on LLRs to reduce decoding complexity by deriving a new update function of path metric for NBPCs and eliminating the path splitting process at perfect polarized (i.e., highly reliable) positions. Simulation results show that the bit error rate of the proposed NBPCs significantly outperforms that of BPCs. In addition, the proposed PPB-SCL decoding obtains about a 40% complexity reduction of SCL decoding for NBPCs.http://www.sciencedirect.com/science/article/pii/S2352864822000050Non-binary polar codeLog-likelihood ratioSuccessive-cancellation listPerfect polarization based-SCLDecoding complexity |
| spellingShingle | Shufeng Li Mingyu Cai Robert Edwards Yao Sun Libiao Jin Research on encoding and decoding of non-binary polar codes over GF(2m) Digital Communications and Networks Non-binary polar code Log-likelihood ratio Successive-cancellation list Perfect polarization based-SCL Decoding complexity |
| title | Research on encoding and decoding of non-binary polar codes over GF(2m) |
| title_full | Research on encoding and decoding of non-binary polar codes over GF(2m) |
| title_fullStr | Research on encoding and decoding of non-binary polar codes over GF(2m) |
| title_full_unstemmed | Research on encoding and decoding of non-binary polar codes over GF(2m) |
| title_short | Research on encoding and decoding of non-binary polar codes over GF(2m) |
| title_sort | research on encoding and decoding of non binary polar codes over gf 2m |
| topic | Non-binary polar code Log-likelihood ratio Successive-cancellation list Perfect polarization based-SCL Decoding complexity |
| url | http://www.sciencedirect.com/science/article/pii/S2352864822000050 |
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