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Mismatched decoding: Error exponents, second-order rates and saddlepoint approximations

Scarlett, J and Martinez, A and Fabregas, AGI (2014) Mismatched decoding: Error exponents, second-order rates and saddlepoint approximations. IEEE Transactions on Information Theory, 60. pp. 2647-2666. ISSN 0018-9448

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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. © 1963-2012 IEEE.

Item Type: Article
Divisions: Div F > Signal Processing and Communications
Depositing User: Cron Job
Date Deposited: 17 Jul 2017 19:32
Last Modified: 22 May 2019 20:39
DOI: 10.1109/TIT.2014.2310453