Analytic approach to coset–leader decoding leads to extension of the Welch–Berlekamp theorem

This paper provides a complete proof of the Welch–Berlekamp theorem on which the Welch–Berlekamp algorithm was founded. By introducing an analytic approach to coset–leader decoders for Reed–Solomon codes, the Welch–Berlekamp key-equation of error corrections is enlarged and a complete proof of the W...

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Bibliographic Details
Published in:Journal of statistical planning and inference Vol. 94; no. 2; pp. 371 - 380
Main Author: Xin, Dingjia
Format: Journal Article Conference Proceeding
Language:English
Published: Lausanne Elsevier B.V 01.04.2001
New York,NY Elsevier Science
Amsterdam
Subjects:
Applied sciences
Coding, codes
Coset–leader decoding
Cyclic codes
Exact sciences and technology
Information, signal and communications theory
Mathematical methods
Reed–Solomon codes
Signal and communications theory
Telecommunications and information theory
Welch–Berlekamp algorithm
Welch–Berlekamp algorithm
Cyclic codes
Coset–leader decoding
Reed–Solomon codes
Reed Solomon code
Cyclic code
Error estimation
Coset leader decoding
Decoding
Algorithm
Communication theory
Interpolation
Weak solution
Example
Error correcting code
BCH code
Error correction
Welch Berlekamp algorithm
Information theory
ISSN:0378-3758, 1873-1171
Online Access:Get full text
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Summary:This paper provides a complete proof of the Welch–Berlekamp theorem on which the Welch–Berlekamp algorithm was founded. By introducing an analytic approach to coset–leader decoders for Reed–Solomon codes, the Welch–Berlekamp key-equation of error corrections is enlarged and a complete proof of the Welch–Berlekamp theorem is derived in a natural way, and the theorem is extended such that the BCH-bound constraint is moved.
ISSN:0378-3758
1873-1171
DOI:10.1016/S0378-3758(00)00267-6