New method of predetermining unified unknown syndrome representations for decoding binary cyclic codes
| Autor: | Yaotsu Chang, Chong-Dao Lee, Jin-Hao Miao, Ming-Haw Jing |
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| Rok vydání: | 2012 |
| Předmět: |
Discrete mathematics
Berlekamp–Welch algorithm Lagrange polynomial Binary number Data_CODINGANDINFORMATIONTHEORY Sequential decoding Rational function Quadratic residue code Computer Science Applications Algebra symbols.namesake ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION symbols Electrical and Electronic Engineering Chinese remainder theorem Decoding methods Computer Science::Information Theory Mathematics |
| Zdroj: | IET Communications. 6:3339-3349 |
| ISSN: | 1751-8636 1751-8628 |
| Popis: | Recently, the unified unknown syndrome representations to decode a class of binary cyclic codes have been developed by using Lagrange interpolation formula (discussed by Chang and Lee in 2010). In this study, a new method by combining the syndrome matrix search and modified Chinese remainder theorem is proposed to express the unified unknown syndrome representation as a rational function in terms of the known syndromes. A computer simulation has been executed to determine the syndrome matrices for binary cyclic codes of lengths less than or equal to 51. Compared to the Lagrange interpolation method, the method presented here substantially reduces the computational time for binary cyclic codes generated by irreducible polynomials. Finally, a complete decoding of the (31, 16, 7) quadratic residue code with inverse-free Berlekamp–Massey algorithm is given as an illustration. |
| Databáze: | OpenAIRE |
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