A Source-Channel Separation Theorem with Application to the Source Broadcast Problem

TL;DR

This paper develops a converse method for the source broadcast problem, establishing a separation theorem that unifies existing results and also proves the optimality of non-separation schemes in certain cases.

Contribution

It introduces a novel converse approach that leverages a separation theorem to unify and extend results in source broadcast problems, including scenarios where separation is suboptimal.

Findings

Separation architecture is optimal for a variant of the source broadcast problem

The method can prove the optimality of non-separation schemes in some scenarios

A necessary condition for the original problem is established via reduction

Abstract

A converse method is developed for the source broadcast problem. Specifically, it is shown that the separation architecture is optimal for a variant of the source broadcast problem and the associated source-channel separation theorem can be leveraged, via a reduction argument, to establish a necessary condition for the original problem, which unifies several existing results in the literature. Somewhat surprisingly, this method, albeit based on the source-channel separation theorem, can be used to prove the optimality of non-separation based schemes and determine the performance limits in certain scenarios where the separation architecture is suboptimal.