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AuthorMohamed, Mostafa Hosnidc.contributor.author
Date of accession2018-01-10T14:05:12Zdc.date.accessioned
Available in OPARU since2018-01-10T14:05:12Zdc.date.available
Year of creation2017dc.date.created
Date of first publication2018-01-10dc.date.issued
AbstractIn this dissertation, new algebraic decoding algorithms for Reed–Solomon codes are developed, all of which use reliability information. The two main scenarios are Reed–Solomon codes defined over finite fields and the complex field. For each scenario, we introduce two new algorithms: a syndrome-based and an interpolation-based decoder. For the first scenario, a syndrome-based method which depends on an intermediate decoding result obtained by the extended Euclidean algorithm is investigated. This method is suitable only for high-rate codes, where one or two additionally correctable errors are valuable. The second method in this scenario, utilizes the same intermediate result to perform an interpolation step similar to the Wu algorithm but with a reduced number of interpolation points. As a results, the complexity of the interpolation step is reduced considerably. The second scenario is the decoding of complex-valued Reed–Solomon codes, which recently gained attention in deterministic Compressed Sensing schemes. They allow the use of known algebraic decoding algorithms for sparse vector reconstruction. It is also possible to extract and exploit intrinsic reliability information. The first decoding method for this scenario performs a multi trial error/erasure decoding procedure to enhance the quality of the reliability information. While the other is a list decoder based on both the Guruswami–Sudan algorithm and generelized minimum distance decoding. The performance of all the aforementioned algorithms has been investigated and compared with similar state-of-the-art algorithms. Without exceptions, their performance surpasses that of their counterparts. The second part of this work has been supported by the German research council Deutsche Forschungsgemeinschaft (DFG) under Grant Bo 867/35-1.dc.description.abstract
Languageendc.language.iso
PublisherUniversität Ulmdc.publisher
LicenseStandarddc.rights
Link to license texthttps://oparu.uni-ulm.de/xmlui/license_v3dc.rights.uri
KeywordFinite fieldsdc.subject
KeywordComplex fielddc.subject
KeywordBerlekamp-Masseydc.subject
KeywordDeterministic compressed sensingdc.subject
KeywordGeneralized Minimum DIstance (GMD) decodingdc.subject
KeywordGuruswami-Sudandc.subject
KeywordChase algorithmdc.subject
KeywordRoth–Ruckensteindc.subject
KeywordGorenstein-Zierlerdc.subject
KeywordRoot-findingdc.subject
KeywordReliability informationdc.subject
KeywordReduced List-Decoderdc.subject
KeywordRecursive enhancementdc.subject
KeywordNewton's methoddc.subject
Dewey Decimal GroupDDC 000 / Computer science, information & general worksdc.subject.ddc
Dewey Decimal GroupDDC 004 / Data processing & computer sciencedc.subject.ddc
LCSHCoding theorydc.subject.lcsh
LCSHReed-Solomon codesdc.subject.lcsh
LCSHFinite fields (Algebra)dc.subject.lcsh
LCSHEuclidean algorithmdc.subject.lcsh
LCSHNewton-Raphson methoddc.subject.lcsh
LCSHRecursive functionsdc.subject.lcsh
TitleAlgebraic decoding over finite and complex fields using reliability informationdc.title
Resource typeDissertationdc.type
Date of acceptance2017-09-26dcterms.dateAccepted
RefereeBossert, Martindc.contributor.referee
RefereeFreudenberger, Jürgendc.contributor.referee
DOIhttp://dx.doi.org/10.18725/OPARU-5289dc.identifier.doi
PPN1011174936dc.identifier.ppn
URNhttp://nbn-resolving.de/urn:nbn:de:bsz:289-oparu-5346-1dc.identifier.urn
GNDCodierungstheoriedc.subject.gnd
GNDRS-Codedc.subject.gnd
GNDGalois-Felddc.subject.gnd
GNDEuklidischer Algorithmusdc.subject.gnd
GNDReliabilitätdc.subject.gnd
FacultyFakultät für Ingenieurwissenschaften, Informatik und Psychologieuulm.affiliationGeneral
InstitutionInstitut für Nachrichtentechnikuulm.affiliationSpecific
Shelfmark print versionW: W-H 15.373uulm.shelfmark
Grantor of degreeFakultät für Ingenieurwissenschaften, Informatik und Psychologieuulm.thesisGrantor
DCMI TypeTextuulm.typeDCMI
CategoryPublikationenuulm.category
Bibliographyuulmuulm.bibliographie
DFG project uulmSPP 1798 Teilprojekt / Komplexwertige Reed-Solomon Codes für deterministisches Compressed Sensing / DFG / 273209895 [BO 867/35]uulm.projectDFG


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