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arXiv · 1303.6166

Mismatched Decoding: Error Exponents, Second-Order Rates and Saddlepoint Approximations

Jonathan Scarlett·Alfonso Martinez·Albert Guillén i Fàbregas
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Abstract

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 i.i.d. 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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Jonathan Scarlett, Alfonso Martinez, Albert Guillén i Fàbregas. 2013-03-25. Mismatched Decoding: Error Exponents, Second-Order Rates and Saddlepoint Approximations. https://arxiv.org/abs/1303.6166

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