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arXiv · 1508.04227

Second-Order Region for Gray-Wyner Network

Shun Watanabe
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Abstract

The coding problem over the Gray-Wyner network is studied from the second-order coding rates perspective. A tilted information density for this network is introduced in the spirit of Kostina-Verdú, and, under a certain regularity condition, the second-order region is characterized in terms of the variance of this tilted information density and the tangent vector of the first-order region. The second-order region is proved by the type method: the achievability part is proved by the type-covering argument, and the converse part is proved by a refinement of the perturbation approach that was used by Gu-Effros to show the strong converse of the Gray-Wyner network. This is the first instance that the second-order region is characterized for a multi-terminal problem where the characterization of the first-order region involves an auxiliary random variable.

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Shun Watanabe. 2015-08-20. Second-Order Region for Gray-Wyner Network. https://doi.org/10.1109/tit.2016.2642985

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