Show simple item record

dc.contributor.advisorRychlik, Mareken_US
dc.contributor.authorMann, Sarah Edge
dc.creatorMann, Sarah Edgeen_US
dc.date.accessioned2013-09-13T17:56:09Z
dc.date.available2013-09-13T17:56:09Z
dc.date.issued2013
dc.identifier.urihttp://hdl.handle.net/10150/301533
dc.description.abstractReed-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.
dc.language.isoenen_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © 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.en_US
dc.subjectKey Equationen_US
dc.subjectRAIDen_US
dc.subjectReed-Solomon codesen_US
dc.subjectWelch-Berelkamp algorithmen_US
dc.subjectApplied Mathematicsen_US
dc.subjecterror correcting codesen_US
dc.titleThe Original View of Reed-Solomon Coding and the Welch-Berlekamp Decoding Algorithmen_US
dc.typetexten_US
dc.typeElectronic Dissertationen_US
thesis.degree.grantorUniversity of Arizonaen_US
thesis.degree.leveldoctoralen_US
dc.contributor.committeememberLin, Kevinen_US
dc.contributor.committeememberWang, Donen_US
dc.contributor.committeememberRychlik, Mareken_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineApplied Mathematicsen_US
thesis.degree.namePh.D.en_US
refterms.dateFOA2018-08-30T14:21:15Z
html.description.abstractReed-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.


Files in this item

Thumbnail
Name:
azu_etd_12891_sip1_m.pdf
Size:
663.7Kb
Format:
PDF

This item appears in the following Collection(s)

Show simple item record