MIMO Wiretap Channels with Arbitrarily Varying Eavesdropper Channel States

TL;DR

This paper investigates the secrecy capacity of MIMO wiretap channels with arbitrarily varying eavesdropper states, establishing universal coding schemes that ensure secure communication regardless of eavesdropper channel variations.

Contribution

It derives the secrecy rate for MIMO wiretap channels with unknown, varying eavesdropper states and demonstrates the existence of universal codes securing against all such states.

Findings

Secrecy rate matches secure degrees of freedom in the worst case.

Universal coding schemes can secure messages against any eavesdropper channel sequence.

Secrecy capacity problems become more tractable with unknown eavesdropper states.

Abstract

In this work, a class of information theoretic secrecy problems is addressed where the eavesdropper channel states are completely unknown to the legitimate parties. In particular, MIMO wiretap channel models are considered where the channel of the eavesdropper is arbitrarily varying over time. Assuming that the number of antennas of the eavesdropper is limited, the secrecy rate of the MIMO wiretap channel in the sense of strong secrecy is derived, and shown to match with the converse in secure degrees of freedom. It is proved that there exists a universal coding scheme that secures the confidential message against any sequence of channel states experienced by the eavesdropper. This yields the conclusion that secure communication is possible regardless of the location or channel states of (potentially infinite number of) eavesdroppers. Additionally, it is observed that, the present setting renders the secrecy capacity problems for multi-terminal wiretap-type channels more tractable as compared the case with full or partial knowledge of eavesdropper channel states. To demonstrate this observation, secure degrees of freedom regions are derived for the Gaussian MIMO multiple access wiretap channel (MIMO MAC-WT) and the Gaussian MIMO broadcast wiretap channel (MIMO BC-WT) where the transmitter(s) and the intended receiver(s) have the same number of antennas.