Secure Broadcasting

TL;DR

This paper extends Wyner's wiretap channel to parallel and fading broadcast channels with multiple receivers, deriving capacity bounds and proposing schemes for secure communication in complex wireless environments.

Contribution

It introduces new capacity bounds and transmission schemes for secure broadcasting over parallel and fading channels with multiple receivers.

Findings

Secrecy capacity bounds are tight for reversely degraded channels.

Positive secure rate is achievable regardless of the number of receivers.

An opportunistic scheme attains sum-capacity in large receiver limits.

Abstract

Wyner's wiretap channel is extended to parallel broadcast channels and fading channels with multiple receivers. In the first part of the paper, we consider the setup of parallel broadcast channels with one sender, multiple intended receivers, and one eavesdropper. We study the situations where the sender broadcasts either a common message or independent messages to the intended receivers. We derive upper and lower bounds on the common-message-secrecy capacity, which coincide when the users are reversely degraded. For the case of independent messages we establish the secrecy sum-capacity when the users are reversely degraded. In the second part of the paper we apply our results to fading channels: perfect channel state information of all intended receivers is known globally, whereas the eavesdropper channel is known only to her. For the common message case, a somewhat surprising result is proven: a positive rate can be achieved independently of the number of intended receivers. For independent messages, an opportunistic transmission scheme is presented that achieves the secrecy sum-capacity in the limit of large number of receivers. Our results are stated for a fast fading channel model. Extensions to the block fading model are also discussed.