Capacity Region Continuity of the Compound Broadcast Channel with Confidential Messages

TL;DR

This paper proves that the capacity region of the compound broadcast channel with confidential messages is continuous with respect to the uncertainty set, ensuring robustness against small variations in channel uncertainty.

Contribution

It establishes the continuity of the capacity region for the compound BCC, a key property for reliable secure communication under channel uncertainty.

Findings

Capacity region depends continuously on the uncertainty set

The model is robust to small variations in channel uncertainty

Ensures reliable and secure communication despite channel variations

Abstract

The compound broadcast channel with confidential messages (BCC) generalizes the BCC by modeling the uncertainty of the channel. For the compound BCC, it is only known that the actual channel realization belongs to a pre-specified uncertainty set of channels and that it is constant during the whole transmission. For reliable and secure communication is necessary to operate at a rate pair within the compound BCC capacity region. Therefore, the question whether small variations of the uncertainty set lead to large losses of the compound BCC capacity region is studied. It is shown that the compound BCC model is robust, i.e., the capacity region depends continuously on the uncertainty set.