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    The Original View of Reed-Solomon Coding and the Welch-Berlekamp Decoding Algorithm

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    Author
    Mann, Sarah Edge
    Issue Date
    2013
    Keywords
    Key Equation
    RAID
    Reed-Solomon codes
    Welch-Berelkamp algorithm
    Applied Mathematics
    error correcting codes
    Advisor
    Rychlik, Marek
    
    Metadata
    Show full item record
    Publisher
    The University of Arizona.
    Rights
    Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
    Abstract
    Reed-Solomon codes are a class of maximum distance separable error correcting codes with known fast error correction algorithms. They have been widely used to assure data integrity for stored data on compact discs, DVDs, and in RAID storage systems, for digital communications channels such as DSL internet connections, and for deep space communications on the Voyager mission. The recent explosion of storage needs for "Big Data'' has generated renewed interest in large storage systems with extended error correction capacity. Reed-Solomon codes have been suggested as one potential solution. This dissertation reviews the theory of Reed-Solomon codes from the perspective taken in Reed and Solomon's original paper on them. It then derives the Welch-Berlekamp algorithm for solving certain polynomial equations, and connects this algorithm to the problem of error correction. The discussion is mathematically rigorous, and provides a complete and consistent discussion of the error correction process. Numerous algorithms for encoding, decoding, erasure recovery, error detection, and error correction are provided and their computational cost is analyzed and discussed thus allowing this dissertation to serve as a manual for engineers interested in implementing Reed-Solomon coding.
    Type
    text
    Electronic Dissertation
    Degree Name
    Ph.D.
    Degree Level
    doctoral
    Degree Program
    Graduate College
    Applied Mathematics
    Degree Grantor
    University of Arizona
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