Mismatched decoding: error exponents, second-order rates and saddlepoint approximations
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- dc.contributor.author Scarlett, Jonathan
- dc.contributor.author Martínez, Alfonso, 1973-
- dc.contributor.author Guillén i Fábregas, A. (Albert)
- dc.date.accessioned 2018-12-07T14:53:14Z
- dc.date.available 2018-12-07T14:53:14Z
- dc.date.issued 2014
- dc.description.abstract This paper considers the problem of channel coding with a given (possibly suboptimal) maximum-metric decoding rule. A cost-constrained random-coding ensemble with multiple auxiliary costs is introduced, and is shown to achieve error exponents and second-order coding rates matching those of constant-composition random coding, while being directly applicable to channels with infinite or continuous alphabets. The number of auxiliary costs required to match the error exponents and second-order rates of constant-composition coding is studied, and is shown to be at most two. For independent identically distributed random coding, asymptotic estimates of two well-known non-asymptotic bounds are given using saddlepoint approximations. Each expression is shown to characterize the asymptotic behavior of the corresponding random-coding bound at both fixed and varying rates, thus unifying the regimes characterized by error exponents, second-order rates, and moderate deviations. For fixed rates, novel exact asymptotics expressions are obtained to within a multiplicative 1+o(1) term. Using numerical examples, it is shown that the saddlepoint approximations are highly accurate even at short block lengths.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 Grants RYC-2011-08150 and TEC2012-38800-C03-03.
- dc.format.mimetype application/pdf
- dc.identifier.citation Scarlett J, Martinez A, Guillén A. Mismatched decoding: error exponents, second-order rates and saddlepoint approximations. IEEE Trans Inf Theory. 2014;60(5):2647-66. DOI: 10.1109/TIT.2014.2310453
- dc.identifier.doi http://dx.doi.org/10.1109/TIT.2014.2310453
- dc.identifier.issn 0018-9448
- dc.identifier.uri http://hdl.handle.net/10230/36017
- dc.language.iso eng
- dc.publisher Institute of Electrical and Electronics Engineers (IEEE)
- dc.relation.ispartof IEEE Transactions on Information Theory. 2014;60(5):2647-66.
- 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/RYC-2011-08150
- 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.2014.2310453
- dc.rights.accessRights info:eu-repo/semantics/openAccess
- dc.subject.keyword Mismatched decoding
- dc.subject.keyword Random coding
- dc.subject.keyword Error exponents
- dc.subject.keyword Second-order coding rate
- dc.subject.keyword Channel dispersion
- dc.subject.keyword Normal approximation
- dc.subject.keyword Saddlepoint approximation
- dc.subject.keyword Exact asymptotics
- dc.subject.keyword Maximum-likelihood decoding
- dc.subject.keyword Finite-length performance
- dc.title Mismatched decoding: error exponents, second-order rates and saddlepoint approximations
- dc.type info:eu-repo/semantics/article
- dc.type.version info:eu-repo/semantics/acceptedVersion