Multiple-Input Multiple-Output Gaussian Broadcast Channels with Common and Confidential Messages

TL;DR

This paper characterizes the secrecy capacity region of a MIMO Gaussian broadcast channel with one common and one confidential message, using a novel channel enhancement technique and extremal entropy inequalities.

Contribution

It introduces a new matrix characterization of the secrecy capacity region for MIMO Gaussian broadcast channels with confidential messages.

Findings

Secrecy capacity region is characterized via channel enhancement.

Enhanced channel is constructed by splitting receiver 1 into virtual receivers.

Extremal entropy inequality is used to derive the capacity region.

Abstract

This paper considers the problem of the multiple-input multiple-output (MIMO) Gaussian broadcast channel with two receivers (receivers 1 and 2) and two messages: a common message intended for both receivers and a confidential message intended only for receiver 1 but needing to be kept asymptotically perfectly secure from receiver 2. A matrix characterization of the secrecy capacity region is established via a channel enhancement argument. The enhanced channel is constructed by first splitting receiver 1 into two virtual receivers and then enhancing only the virtual receiver that decodes the confidential message. The secrecy capacity region of the enhanced channel is characterized using an extremal entropy inequality previously established for characterizing the capacity region of a degraded compound MIMO Gaussian broadcast channel.