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• W2906674516 abstract "A strong converse shows that no procedure can beat the asymptotic (as blocklength $ntoinfty$) fundamental limit of a given information-theoretic problem for any fixed error probability. A second-order converse strengthens this conclusion by showing that the asymptotic fundamental limit cannot be exceeded by more than $O(tfrac{1}{sqrt{n}})$. While strong converses are achieved in a broad range of information-theoretic problems by virtue of the blowing-up method---a powerful methodology due to Ahlswede, G'acs and Korner (1976) based on concentration of measure---this method is fundamentally unable to attain second-order converses and is restricted to finite-alphabet settings. Capitalizing on reverse hypercontractivity of Markov semigroups and functional inequalities, this paper develops the smoothing-out method, an alternative to the blowing-up approach that does not rely on finite alphabets and that leads to second-order converses in a variety of information-theoretic problems that were out of reach of previous methods." @default.
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• W2906674516 date "2018-12-25" @default.
• W2906674516 modified "2023-10-18" @default.
• W2906674516 title "Second-Order Converses via Reverse Hypercontractivity" @default.
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• W2906674516 doi "https://doi.org/10.48550/arxiv.1812.10129" @default.
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