2026-04-14T03:52:33Zhttps://recercat.cat/oai/request

oai:recercat.cat:10230/360172025-12-18T01:27:17Zcom_2072_6col_2072_452952

00925njm 22002777a 4500 dc Scarlett, Jonathan author Martínez, Alfonso, 1973- author Guillén i Fábregas, A. (Albert) author 2018-12-07T14:53:14Z 2018-12-07T14:53:14Z 2014 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. 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. Mismatched decoding Random coding Error exponents Second-order coding rate Channel dispersion Normal approximation Saddlepoint approximation Exact asymptotics Maximum-likelihood decoding Finite-length performance Mismatched decoding: error exponents, second-order rates and saddlepoint approximations