MIMO Broadcast Channel with Arbitrarily Varying Eavesdropper Channel: Secrecy Degrees of Freedom

A two-receiver MIMO broadcast-wiretap channel is considered where the channel state of the eavesdropper is arbitrarily varying. It is assumed that the eavesdropper knows this channel state perfectly whereas the legitimate nodes have no knowledge of it. It is further assumed that the eavesdropper experiences no additive noise. The channel between the transmitter and the two legitimate receivers is a constant MIMO Gaussian broadcast channel. This paper establishes the secrecy degrees of freedom region for transmitting a common-confidential message as well as a private- confidential message to each receiver. It is observed that a straightforward extension of single user random binning does not achieve the optimal secrecy degrees of freedom (s.d.o.f.) region. The proposed coding scheme that achieves the s.d.o.f. region involves simultaneous diagonalization of the channel matrices of the two legitimate receivers using the generalized singular value decomposition (GSVD) as well as a particular \emph{structured binning} across codebooks that minimizes the rate of the fictitious message. While the focus is on achieving weak secrecy for ease of exposition, an outline is provided on how the results can be extended for achieving strong secrecy.