Mismatched decoding: error exponents, second-order rates and saddlepoint approximations
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-...
| Autores: | , , |
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| Tipo de documento: | artigo |
| Estado: | Versión aceptada para publicación |
| Data de publicação: | 2014 |
| País: | España |
| Recursos: | Universitat Pompeu Fabra |
| Repositório: | Repositorio Digital de la UPF |
| OAI Identifier: | oai:repositori.upf.edu:10230/36017 |
| Acesso em linha: | http://hdl.handle.net/10230/36017 http://dx.doi.org/10.1109/TIT.2014.2310453 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Mismatched decoding Random coding Error exponents Second-order coding rate Channel dispersion Normal approximation Saddlepoint approximation Exact asymptotics Maximum-likelihood decoding Finite-length performance |
| Resumo: | 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. |
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