2 research outputs found
Second-Order Region for Gray-Wyner Network
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.Comment: 24 pages, 2 figures; some minor modifications in v
Strong Converse using Change of Measure Arguments
The strong converse for a coding theorem shows that the optimal asymptotic
rate possible with vanishing error cannot be improved by allowing a fixed
error. Building on a method introduced by Gu and Effros for centralized coding
problems, we develop a general and simple recipe for proving strong converse
that is applicable for distributed problems as well. Heuristically, our proof
of strong converse mimics the standard steps for proving a weak converse,
except that we apply those steps to a modified distribution obtained by
conditioning the original distribution on the event that no error occurs. A key
component of our recipe is the replacement of the hard Markov constraints
implied by the distributed nature of the problem with a soft information cost
using a variational formula introduced by Oohama. We illustrate our method by
providing a short proof of the strong converse for the Wyner-Ziv problem and
strong converse theorems for interactive function computation, common
randomness and secret key agreement, and the wiretap channel; the latter three
strong converse problems were open prior to this work.Comment: 35 pages, no figure; v2 updated reference