New Results on Multiple-Input Multiple-Output Broadcast Channels with Confidential Messages

TL;DR

This paper advances understanding of MIMO Gaussian broadcast channels with confidential messages by providing new capacity-equivocation and capacity region characterizations, extending previous secrecy results to more general and complex scenarios.

Contribution

It offers a matrix characterization of the capacity-equivocation region for MIMO wiretap channels and a complete capacity region for broadcast channels with multiple confidential messages.

Findings

Extended the secrecy capacity to imperfect secrecy settings.

Precisely characterized the capacity region for complex MIMO broadcast channels.

Generalized previous results to include multiple confidential messages.

Abstract

This paper presents two new results on multiple-input multiple-output (MIMO) Gaussian broadcast channels with confidential messages. First, the problem of the MIMO Gaussian wiretap channel is revisited. A matrix characterization of the capacity-equivocation region is provided, which extends the previous result on the secrecy capacity of the MIMO Gaussian wiretap channel to the general, possibly imperfect secrecy setting. Next, the problem of MIMO Gaussian broadcast channels with two receivers and three independent messages: a common message intended for both receivers, and two confidential messages each intended for one of the receivers but needing to be kept asymptotically perfectly secret from the other, is considered. A precise characterization of the capacity region is provided, generalizing the previous results which considered only two out of three possible messages.