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-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.

24 pages, 2 figures; some minor modifications in v2

References in corpus (3)

• On the Dispersions of Three Network Information Theory Problems
• Second-Order Coding Rates for Channels with State
• Second-Order Asymptotics for the Gaussian MAC with Degraded Message Sets

Cited by in corpus (5)

• On Finite Blocklength Lossy Source Coding
• The Dispersion of the Gauss-Markov Source
• First- and Second-Order Hypothesis Testing for Mixed Memoryless Sources with General Mixture
• Nonstationary Gauss-Markov Processes: Parameter Estimation and Dispersion
• One-Shot Distributed Source Simulation: As Quantum as it Can Get