Scarlett, JonathanMartínez, Alfonso, 1973-Guillén i Fábregas, A. (Albert)2018-12-072018-12-072014Scarlett 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.2014.23104530018-9448http://hdl.handle.net/10230/36017This 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.application/pdfeng© 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.2014.2310453info:eu-repo/semantics/articlehttp://dx.doi.org/10.1109/TIT.2014.2310453Mismatched decodingRandom codingError exponentsSecond-order coding rateChannel dispersionNormal approximationSaddlepoint approximationExact asymptoticsMaximum-likelihood decodingFinite-length performanceinfo:eu-repo/semantics/openAccess