MIMO Gaussian Broadcast Channels with Common, Private and Confidential Messages

TL;DR

This paper characterizes the secrecy-capacity region of a two-user MIMO Gaussian broadcast channel with common, private, and confidential messages, using Gaussian inputs and dirty-paper coding techniques.

Contribution

It provides a complete characterization of the secrecy-capacity region for this channel model, demonstrating the optimality of Gaussian inputs and DPC-based strategies.

Findings

Inner and outer bounds coincide, establishing the capacity region.

Gaussian inputs achieve the boundary points of the capacity region.

DPC cancels non-confidential signals, simplifying the coding scheme.

Abstract

The two-user multiple-input multiple-output (MIMO) Gaussian broadcast channel (BC) with common, private and confidential messages is considered. The transmitter sends a common message to both users, a confidential message to User 1 and a private (non-confidential) message to User 2. The secrecy-capacity region is characterized by showing that certain inner and outer bounds coincide and that the boundary points are achieved by Gaussian inputs, which enables the development of a tight converse. The proof relies on factorization of upper concave envelopes and a variant of dirty-paper coding (DPC). It is shown that the entire region is exhausted by using DPC to cancel out the signal of the non-confidential message at Receiver 1, thus making DPC against the signal of the confidential message unnecessary. A numerical example illustrates the secrecy-capacity results.