On the Capacity Region for Secure Index Coding

TL;DR

This paper investigates the secure index coding problem, establishing bounds on the capacity region considering security constraints, and proposes a secure coding scheme that achieves this capacity for small message sets.

Contribution

It introduces an outer bound and a secure composite coding scheme for the index coding problem with security constraints, including conditions for achievability.

Findings

Outer bound on secure capacity region established

Secure composite coding scheme proposed and analyzed

Capacity region determined for problems with four or fewer messages

Abstract

We study the index coding problem in the presence of an eavesdropper, where the aim is to communicate without allowing the eavesdropper to learn any single message aside from the messages it may already know as side information. We establish an outer bound on the underlying secure capacity region of the index coding problem, which includes polymatroidal and security constraints, as well as the set of additional decoding constraints for legitimate receivers. We then propose a secure variant of the composite coding scheme, which yields an inner bound on the secure capacity region of the index coding problem. For the achievability of secure composite coding, a secret key with vanishingly small rate may be needed to ensure that each legitimate receiver who wants the same message as the eavesdropper, knows at least two more messages than the eavesdropper. For all securely feasible index coding problems with four or fewer messages, our numerical results establish the secure index coding capacity region.