Efficient decoding of the (23, 12, 7) Golay code up to five errors
A novel and efficient algorithm for decoding the (23, 12, 7) Golay code with the five-error correcting capability is developed. Core to the key idea is innovatively utilizing the relationship of syndromes among error patterns, which is derived from the property of perfect code. Consequently, two met...
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| Published in: | Information sciences Vol. 253; pp. 170 - 178 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
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20.12.2013
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| Abstract | A novel and efficient algorithm for decoding the (23, 12, 7) Golay code with the five-error correcting capability is developed. Core to the key idea is innovatively utilizing the relationship of syndromes among error patterns, which is derived from the property of perfect code. Consequently, two methods of fast searching candidate codewords are proposed, both of which only perform the algebraic hard decision decoder once, rather than iterative decoding of Chase-like algorithm. With the set of the possible codewords, the most likely one is chosen as an output codeword based on the correlation metric. In comparison to Chase-2 algorithm, simulation results over the AWGN channel reveal the decoding times of the proposed algorithm equipped with codeword matching and syndrome-group search are reduced by 25% and 75%, respectively. In terms of the percentage of correct decoding, it turns out that the proposed algorithm outperforms Chase-2 algorithm, especially in the error-prone transmission environment. These favorable results demonstrate that the new algorithm is beneficial to implement in practice. |
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| AbstractList | A novel and efficient algorithm for decoding the (23, 12, 7) Golay code with the five-error correcting capability is developed. Core to the key idea is innovatively utilizing the relationship of syndromes among error patterns, which is derived from the property of perfect code. Consequently, two methods of fast searching candidate codewords are proposed, both of which only perform the algebraic hard decision decoder once, rather than iterative decoding of Chase-like algorithm. With the set of the possible codewords, the most likely one is chosen as an output codeword based on the correlation metric. In comparison to Chase-2 algorithm, simulation results over the AWGN channel reveal the decoding times of the proposed algorithm equipped with codeword matching and syndrome-group search are reduced by 25% and 75%, respectively. In terms of the percentage of correct decoding, it turns out that the proposed algorithm outperforms Chase-2 algorithm, especially in the error-prone transmission environment. These favorable results demonstrate that the new algorithm is beneficial to implement in practice. |
| Author | Lee, Hung-Peng Chang, Hsin-Chiu Chu, Shao-I |
| Author_xml | – sequence: 1 givenname: Hung-Peng surname: Lee fullname: Lee, Hung-Peng email: hpl@fotech.edu.tw organization: Dept. of Information Science and Information Engineering, Fortune Institute of Technology, Kaohsiung City 831, Taiwan, ROC – sequence: 2 givenname: Shao-I surname: Chu fullname: Chu, Shao-I organization: Dept. of Electronic Engineering, National Kaohsiung University of Applied Sciences, Kaohsiung City 807, Taiwan, ROC – sequence: 3 givenname: Hsin-Chiu surname: Chang fullname: Chang, Hsin-Chiu organization: Dept. of Information Science and Information Engineering, Fortune Institute of Technology, Kaohsiung City 831, Taiwan, ROC |
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| Cites_doi | 10.1109/TIT.1987.1057262 10.1049/iet-com:20080037 10.1080/00207729508929077 10.1109/TIT.1964.1053649 10.1109/TIT.1972.1054746 10.1002/ett.1491 10.1016/j.ins.2012.02.020 10.1109/GLOCOM.2005.1577867 10.1016/j.ins.2010.08.015 |
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| References_xml | – reference: W.K. Su, P.Y. Shih, T.C. Lin, T.K. Truong, G. Dubney, On soft-decoding of the (24, 12, 8) Golay code, in: IEEE TENCON 2007, Taipei, Taiwan, ROC, 2007, pp. 1–4. – volume: 37 start-page: 637 year: 1949 ident: b0025 article-title: Notes on digital coding publication-title: Proceedings IEEE – volume: 10 start-page: 134 year: 1964 end-page: 139 ident: b0030 article-title: A decoding procedure for multiple-error correction cyclic codes publication-title: IEEE Transaction on Information Theory – volume: 197 start-page: 215 year: 2012 end-page: 222 ident: b0040 article-title: A cyclic weight algorithm of decoding the (47, 24, 11) quadratic residue code publication-title: Information Sciences – volume: 137 start-page: 202 year: 1990 end-page: 206 ident: b0055 article-title: Decoding the (24, 12, 8) Golay code publication-title: Processings IEE – reference: G. Dubney, I.S. 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| SubjectTerms | Error pattern Golay code Soft-decoding Syndrome |
| Title | Efficient decoding of the (23, 12, 7) Golay code up to five errors |
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