Title:
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Mismatched decoding: error exponents, second-order rates and saddlepoint approximations
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Author:
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Scarlett, Jonathan; Martinez, Alfonso; Guillén i Fàbregas, Albert
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Abstract:
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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. |
Abstract:
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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. |
Subject(s):
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-Mismatched decoding -Random coding -Error exponents -Second-order coding rate -Channel dispersion -Normal approximation -Saddlepoint approximation -Exact asymptotics -Maximum-likelihood decoding -Finite-length performance |
Rights:
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© 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 |
Document type:
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Article Article - Accepted version |
Published by:
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Institute of Electrical and Electronics Engineers (IEEE)
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