Expurgated random-coding ensembles: exponents, refinements and connections

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• dc.contributor.author Scarlett, Jonathan
• dc.contributor.author Peng, Li
• dc.contributor.author Merhav, Neri
• dc.contributor.author Martínez, Alfonso, 1973-
• dc.contributor.author Guillén i Fábregas, A. (Albert)
• dc.date.accessioned 2018-12-07T14:53:10Z
• dc.date.available 2018-12-07T14:53:10Z
• dc.date.issued 2014
• dc.description.abstract This paper studies expurgated random-coding bounds and exponents for channel coding with a given (possibly suboptimal) decoding rule. Variations of Gallager's analysis are presented, yielding several asymptotic and nonasymptotic bounds on the error probability for an arbitrary codeword distribution. A simple nonasymptotic bound is shown to attain an exponent of Csiszár and Körner under constant-composition coding. Using Lagrange duality, this exponent is expressed in several forms, one of which is shown to permit a direct derivation via cost-constrained coding that extends to infinite and continuous alphabets. The method of type class enumeration is studied, and it is shown that this approach can yield improved exponents and better tightness guarantees for some codeword distributions. A generalization of this approach is shown to provide a multiletter exponent that extends immediately to channels with memory.en
• dc.description.sponsorship This work was supported in part by the European Research Council under Grant 259663, in part by the European Union’s 7th Framework Programme under Grant 303633, and in part by the Spanish Ministry of Economy and Competitiveness under Grant RYC-2011-08150 and Grant TEC2012-38800-C03-03. The work of N. Merhav was supported by the Israel Science Foundation under Grant 412/12.
• dc.format.mimetype application/pdf
• dc.identifier.citation Scarlett J, Peng L, Merhav N, Martinez A, Guillén A. Expurgated random-coding ensembles: exponents, refinements and connections. IEEE Trans Inf Theory. 2014;60(8):4449-62. DOI: 10.1109/TIT.2014.2322033
• dc.identifier.doi http://dx.doi.org/10.1109/TIT.2014.2322033
• dc.identifier.issn 0018-9448
• dc.identifier.uri http://hdl.handle.net/10230/36016
• dc.language.iso eng
• dc.publisher Institute of Electrical and Electronics Engineers (IEEE)
• dc.relation.ispartof IEEE Transactions on Information Theory 2014;60(8):4449-62.
• dc.relation.projectID info:eu-repo/grantAgreement/EC/FP7/259663
• dc.relation.projectID info:eu-repo/grantAgreement/EC/FP7/303633
• dc.relation.projectID info:eu-repo/grantAgreement/ES/3PN/RYC2011-08150
• dc.relation.projectID info:eu-repo/grantAgreement/ES/3PN/TEC2012-38800-C03-03
• dc.rights © 2014 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. The final published article can be found at http://dx.doi.org/10.1109/TIT.2014.2322033
• dc.rights.accessRights info:eu-repo/semantics/openAccess
• dc.subject.keyword Expurgated error exponents
• dc.subject.keyword Reliability function
• dc.subject.keyword Random coding
• dc.subject.keyword Mismatched decoding
• dc.subject.keyword Maximum-likelihood decoding
• dc.subject.keyword Type class enumeration
• dc.title Expurgated random-coding ensembles: exponents, refinements and connections
• dc.type info:eu-repo/semantics/article
• dc.type.version info:eu-repo/semantics/acceptedVersion