Second-Order Region for Gray-Wyner Network
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-Verd\'u, 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.
Cite
@article{arxiv.1508.04227,
title = {Second-Order Region for Gray-Wyner Network},
author = {Shun Watanabe},
journal= {arXiv preprint arXiv:1508.04227},
year = {2017}
}
Comments
24 pages, 2 figures; some minor modifications in v2