Algebraic list-decoding of error-correcting codes

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" Algebraic list-decoding of error-correcting codes "
Parvaresh, Farzad

Document Type	:	Latin Dissertation
Language of Document	:	English
Record Number	:	906016
Doc. No	:	TL68q346tn
Main Entry	:	Parvaresh, Farzad
Title & Author	:	Algebraic list-decoding of error-correcting codes\ Parvaresh, Farzad
College	:	UC San Diego
Date	:	2007
student score	:	2007
Abstract	:	This dissertation is concerned with algebraic list- decoding of error-correcting codes. During the past decade, significant advances in this are were achieved. The breakthrough papers of Sudan, Guruswami & Sudan, and Koetter & Vardy showed that the well-known Reed-Solomon (and other algebraic) codes can correct many more errors - - in the list-decoding sense -- than previously thought possible. Herein, we extend the theory developed in these seminal papers, and improve upon the results reported therein. We first extend the bivariate polynomial interpolation method of Guruswami-Sudan to multivariate interpolation decoding. To this end, we develop a new decoding algorithm for Reed-Solomon codes, which decodes some M codewords together. We show that if the channel errors are synchronized then, with high probability, our multivariate interpolation decoding algorithm corrects up to
Added Entry	:	UC San Diego