The capacity region of a product of two unmatched Gaussian broadcast channels with three particular messages and a common message

TL;DR

This paper characterizes the capacity region of a Gaussian broadcast channel with unmatched components, demonstrating that superposition coding and Gaussian signaling suffice to achieve all capacity points.

Contribution

It establishes that for a specific Gaussian broadcast channel with three messages, superposition coding and Gaussian signaling are sufficient for capacity achievement.

Findings

Superposition coding achieves the capacity region.

Gaussian signaling is sufficient for optimality.

Capacity region characterized for the specific channel model.

Abstract

This paper considers a Gaussian broadcast channel with two unmatched degraded components, three particular messages, and a common message that is intended for all three receivers. It is shown that for this channel superposition coding and Gaussian signalling is sufficient to achieve every point in the capacity region.