Shannon Bounds on Lossy Gray-Wyner Networks

TL;DR

This paper derives bounds on the rate trade-offs in lossy Gray-Wyner networks with mean-squared error, providing exact solutions for Gaussian sources and partial bounds for Gaussian channel models.

Contribution

It introduces new upper and lower bounds for the rate region in lossy Gray-Wyner networks, extending Shannon bounds to this setting.

Findings

Bounds exactly characterize the rate region for Gaussian sources.

Bounds partially apply to Gaussian channel models.

The bounds are inspired by Shannon bounds on rate-distortion.

Abstract

The Gray-Wyner network subject to a fidelity criterion is studied. Upper and lower bounds for the trade-offs between the private sum-rate and the common rate are obtained for arbitrary sources subject to mean-squared error distortion. The bounds meet exactly, leading to the computation of the rate region, when the source is jointly Gaussian. They meet partially when the sources are modeled via an additive Gaussian "channel". The bounds are inspired from the Shannon bounds on the rate-distortion problem.