Outer Bounds on the Admissible Source Region for Broadcast Channels with Correlated Sources

TL;DR

This paper introduces two new outer bounds on the admissible source region for broadcast channels with correlated sources, improving existing bounds and fully characterizing the case with conditionally independent sources.

Contribution

It presents two novel outer bounds for the admissible source region, one tighter than previous bounds and one complete for conditionally independent sources.

Findings

One outer bound is strictly tighter than Gohari and Anantharam's.

The second outer bound fully characterizes the region for conditionally independent sources.

The bounds are derived from necessary conditions using virtual and physical broadcast channel comparisons.

Abstract

Two outer bounds on the admissible source region for broadcast channels with correlated sources are presented: the first one is strictly tighter than the existing outer bound by Gohari and Anantharam while the second one provides a complete characterization of the admissible source region in the case where the two sources are conditionally independent given the common part. These outer bounds are deduced from the general necessary conditions established for the lossy source broadcast problem via suitable comparisons between the virtual broadcast channel (induced by the source and the reconstructions) and the physical broadcast channel.