Correlated Sources over Broadcast Channels

TL;DR

This paper revisits the problem of transmitting correlated sources over broadcast channels, offering a new characterization of conditions for reliable transmission and proposing a simplified coding scheme based on joint typicality.

Contribution

It provides an alternative, more straightforward characterization of reliable transmission conditions and introduces a minimalistic coding scheme that avoids complex coding techniques.

Findings

Includes results of Marton and Gray-Wyner in the new characterization

Proposes a simple joint typicality-based coding scheme

Uses a new multivariate covering lemma and Fourier--Motzkin elimination

Abstract

The problem of reliable transmission of correlated sources over the broadcast channel, originally studied by Han and Costa, is revisited. An alternative characterization of their sufficient condition for reliable transmission is given, which includes results of Marton for channel coding over broadcast channels and of Gray and Wyner for distributed source coding. A ``minimalistic'' coding scheme is presented, which is based on joint typicality encoding and decoding, without requiring the use of Cover's superposition coding, random hashing, and common part between two sources. The analysis of the coding scheme is also conceptually simple and relies on a new multivariate covering lemma and an application of the Fourier--Motzkin elimination procedure.