A new Reed-Solomon code decoding algorithm based on Newton's interpolation
A Reed-Solomon code decoding algorithm based on Newton's interpolation is presented. This algorithm has as main application fast generalized-minimum-distance decoding of Reed-Solomon codes. It uses a modified Berlekamp-Massey algorithm to perform all necessary generalized-minimum-distance decod...
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| Published in | IEEE transactions on information theory Vol. 39; no. 2; pp. 358 - 365 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
New York, NY
IEEE
01.03.1993
Institute of Electrical and Electronics Engineers |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0018-9448 |
| DOI | 10.1109/18.212267 |
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| Abstract | A Reed-Solomon code decoding algorithm based on Newton's interpolation is presented. This algorithm has as main application fast generalized-minimum-distance decoding of Reed-Solomon codes. It uses a modified Berlekamp-Massey algorithm to perform all necessary generalized-minimum-distance decoding steps in only one run. With a time-domain form of the new decoder the overall asymptotic generalized-minimum-distance decoding complexity becomes O(dn), with n the length and d the distance of the code (including the calculation of all error locations and values). This asymptotic complexity is optimal. Other applications are the possibility of fast decoding of Reed-Solomon codes with adaptive redundancy and a general parallel decoding algorithm with zero delay.< > |
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| AbstractList | A Reed-Solomon code decoding algorithm based on Newton's interpolation is presented. This algorithm has as main application fast generalized-minimum-distance decoding of Reed-Solomon codes. It uses a modified Berlekamp-Massey algorithm to perform all necessary generalized-minimum-distance decoding steps in only one run. With a time-domain form of the new decoder the overall asymptotic generalized-minimum-distance decoding complexity becomes O(dn), with n the length and d the distance of the code (including the calculation of all error locations and values). This asymptotic complexity is optimal. Other applications are the possibility of fast decoding of Reed-Solomon codes with adaptive redundancy and a general parallel decoding algorithm with zero delay.< > A Reed-Solomon code decoding algorithm based on Newton's interpolation is presented. This algorithm has as main application fast generalized-minimum-distance decoding of Reed-Solomon codes. It uses a modified Berlekamp-Massey algorithm to perform all necessary generalized-minimum-distance decoding steps in only one run. With a time-domain form of the new decoder the overall asymptotic generalized-minimum-distance decoding complexity becomes < e1 > O < /e1 > ( < e1 > dn < /e1 > ), with < e1 > n < /e1 > the length and < e1 > d < /e1 > the distance of the code (including the calculation of all error locations and values). This asymptotic complexity is optimal. Other applications are the possibility of fast decoding of Reed-Solomon codes with adaptive redundancy and a general parallel decoding algorithm with zero delay A new Reed-Solomon code decoding algorithm based on Newton's interpolation is presented. This algorithm has as main application fast generalized-minimum distance decoding of Reed-Solomon codes. It uses a modified Berlekamp-Massey algorithm to perform all necessary generalized-minimum-distance decoding steps in only one run. With a time-domain form of the new decoder the overall asymptotic generalized-minimum-distance decoding complexity becomes O(dn) with n the length and d the distance of the code (including the calculation of all error locations and values). This asymptotic complexity is optimal. Other applications are the possibility of fast decoding of Reed-Solomon codes with adaptive redundancy and a general parallel decoding algorithm with zero delay. |
| Author | Sorger, U.K. |
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| Cites_doi | 10.1109/TIT.1969.1054260 10.1109/TIT.1979.1055988 10.1109/18.61132 10.1109/49.29613 |
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| Keywords | Reed Solomon code Interpolation Parallel algorithm Minimal distance Decoding |
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| References | dorsch (ref3) 1983 ref12 ref14 ref11 macwilliams (ref10) 1977 sokolnikov (ref13) 1966 forney (ref6) 1966 ref9 dumer (ref4) 1991 berlekamp (ref1) 1986 kabatyansky (ref5) 1991 blahut (ref2) 1984 henkel (ref7) 1989 zinoviev (ref15) 1981; 17 kovalev (ref8) 1986; 22 |
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| SubjectTerms | Applied sciences Coding, codes Decoding Delay Encoding Equations Exact sciences and technology Fourier transforms Information, signal and communications theory Interpolation Polynomials Redundancy Reed-Solomon codes Signal and communications theory Telecommunications and information theory Time domain analysis |
| Title | A new Reed-Solomon code decoding algorithm based on Newton's interpolation |
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