Algebraic decoding of the (41, 21, 9) quadratic residue code without determining the unknown syndromes
Quadratic residue (QR) codes have a high prospect on error correction for reliable data conveyance over channel with noise. This paper presents a fast algebraic scheme for decoding the binary (41, 21, 9) QR code for correcting up to 4 errors on an one-case-by-one-case basis, in which the calculation...
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| Vydáno v: | Physical communication Ročník 42; s. 101135 |
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Elsevier B.V
01.10.2020
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| ISSN: | 1874-4907, 1876-3219 |
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| Abstract | Quadratic residue (QR) codes have a high prospect on error correction for reliable data conveyance over channel with noise. This paper presents a fast algebraic scheme for decoding the binary (41, 21, 9) QR code for correcting up to 4 errors on an one-case-by-one-case basis, in which the calculation of unknown syndromes is eliminated and the conditions for checking for the various numbers of errors that exist in the received word are also simplified compared to those from Lin T. C. et al.’s algorithm, which is a traditional algebraic decoding algorithm (ADA). The computational complexity of the decoder performing the binary (41, 21, 9) QR code is analyzed thoroughly, which demonstrates that the proposed decoding scheme is faster, simpler, and more suitable for implementation than Lin T. C. et al.’s algorithm. Numerical emulation results demonstrate that the proposed decoding scheme achieves the same error-rate performance as Lin T. C. et al.’s algorithm, but it has a significantly decreased the complexity of this decoder in terms of the CPU time. |
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| AbstractList | Quadratic residue (QR) codes have a high prospect on error correction for reliable data conveyance over channel with noise. This paper presents a fast algebraic scheme for decoding the binary (41, 21, 9) QR code for correcting up to 4 errors on an one-case-by-one-case basis, in which the calculation of unknown syndromes is eliminated and the conditions for checking for the various numbers of errors that exist in the received word are also simplified compared to those from Lin T. C. et al.’s algorithm, which is a traditional algebraic decoding algorithm (ADA). The computational complexity of the decoder performing the binary (41, 21, 9) QR code is analyzed thoroughly, which demonstrates that the proposed decoding scheme is faster, simpler, and more suitable for implementation than Lin T. C. et al.’s algorithm. Numerical emulation results demonstrate that the proposed decoding scheme achieves the same error-rate performance as Lin T. C. et al.’s algorithm, but it has a significantly decreased the complexity of this decoder in terms of the CPU time. |
| ArticleNumber | 101135 |
| Author | Luo, Chunlan Xing, Song Wu, Yi Yang, Zheng Chang, Hsin-chiu |
| Author_xml | – sequence: 1 givenname: Chunlan surname: Luo fullname: Luo, Chunlan email: chunlanlou@yeah.net organization: Key Laboratory of Opto Electronic Science and Technology for Medicine of Ministry of Education, Fujian Provincial Key Laboratory of Photonics Technology, and Fujian Provincial Engineering Technology Research Center of Photoelectric Sensing Application, Fujian Normal University, Fuzhou, China – sequence: 2 givenname: Yi surname: Wu fullname: Wu, Yi email: wuyi@fjnu.edu.cn organization: Key Laboratory of Opto Electronic Science and Technology for Medicine of Ministry of Education, Fujian Provincial Key Laboratory of Photonics Technology, and Fujian Provincial Engineering Technology Research Center of Photoelectric Sensing Application, Fujian Normal University, Fuzhou, China – sequence: 3 givenname: Hsin-chiu surname: Chang fullname: Chang, Hsin-chiu email: newballch@gmail.com organization: Key Laboratory of Opto Electronic Science and Technology for Medicine of Ministry of Education, Fujian Provincial Key Laboratory of Photonics Technology, and Fujian Provincial Engineering Technology Research Center of Photoelectric Sensing Application, Fujian Normal University, Fuzhou, China – sequence: 4 givenname: Zheng surname: Yang fullname: Yang, Zheng email: zyfjnu@163.com organization: Key Laboratory of Opto Electronic Science and Technology for Medicine of Ministry of Education, Fujian Provincial Key Laboratory of Photonics Technology, and Fujian Provincial Engineering Technology Research Center of Photoelectric Sensing Application, Fujian Normal University, Fuzhou, China – sequence: 5 givenname: Song surname: Xing fullname: Xing, Song email: sxing@exchange.calstatela.edu organization: Information Systems Department, California State University, Los Angeles, USA |
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| Cites_doi | 10.1109/18.915677 10.1109/TCOMM.2009.07.060542 10.1109/TIT.1987.1057262 10.1016/j.ins.2009.06.002 10.1109/TIT.1964.1053699 10.1109/18.333854 10.1109/TCOMM.2003.816994 10.1109/TIT.2008.929956 10.1109/18.135639 10.1109/TC.1985.1676616 |
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| Keywords | Quadratic residue codes Fast algebraic decoding algorithm Error pattern Syndrome |
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| References | Lin, Truong, Lee, Chang (b8) 2009; 179 Chien (b11) 1964; 10 Reed, Truong, Chen, Yin (b9) 1992; 38 He, Reed, Truong, Chen (b4) 2001; 47 Elia (b3) 1987; 33 Prange (b1) 1958 Dubney, Reed, Truong, Yang (b5) 2009; 57 Wang, Truong, Shao, Deutsch, Omura, Reed (b14) 1985; 34 Chen, Truong, Chang, Lee, Chen (b10) 2007; 23 Wicker (b2) 1994 Truong, Shih, Su, Lee, Chang (b7) 2008; 54 Feng, Tzeng (b13) 1994; 40 Chang, Truong, Reed, Cheng, Lee (b6) 2003; 51 Berlekamp (b12) 1968 Chen (10.1016/j.phycom.2020.101135_b10) 2007; 23 Elia (10.1016/j.phycom.2020.101135_b3) 1987; 33 Wang (10.1016/j.phycom.2020.101135_b14) 1985; 34 Reed (10.1016/j.phycom.2020.101135_b9) 1992; 38 Lin (10.1016/j.phycom.2020.101135_b8) 2009; 179 Chang (10.1016/j.phycom.2020.101135_b6) 2003; 51 Berlekamp (10.1016/j.phycom.2020.101135_b12) 1968 Prange (10.1016/j.phycom.2020.101135_b1) 1958 Chien (10.1016/j.phycom.2020.101135_b11) 1964; 10 Truong (10.1016/j.phycom.2020.101135_b7) 2008; 54 He (10.1016/j.phycom.2020.101135_b4) 2001; 47 Feng (10.1016/j.phycom.2020.101135_b13) 1994; 40 Wicker (10.1016/j.phycom.2020.101135_b2) 1994 Dubney (10.1016/j.phycom.2020.101135_b5) 2009; 57 |
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| SubjectTerms | Error pattern Fast algebraic decoding algorithm Quadratic residue codes Syndrome |
| Title | Algebraic decoding of the (41, 21, 9) quadratic residue code without determining the unknown syndromes |
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