The MIMO wiretap channel

We study the MIMO wiretap channel, a MIMO broadcast channel where the transmitter sends some confidential information to one user which is a legitimate receiver, while the other user is an eavesdropper. Perfect secrecy is achieved when the transmitter and the legitimate receiver can communicate at some positive rate, while ensuring that the eavesdropper gets zero bits of information. In this paper, we compute the perfect secrecy capacity of the multiple antenna MIMO broadcast channel, where the number of antennas is arbitrary for both the transmitter and the two receivers. Our technique involves a careful study of a Sato-like upper bound via the solution of a certain algebraic Riccati equation

Towards the Secrecy Capacity of the Gaussian MIMO Wire-tap Channel: The 2-2-1 Channel

We find the secrecy capacity of the 2-2-1 Gaussian MIMO wire-tap channel, which consists of a transmitter and a receiver with two antennas each, and an eavesdropper with a single antenna. We determine the secrecy capacity of this channel by proposing an achievable scheme and then developing a tight upper bound that meets the proposed achievable secrecy rate. We show that, for this channel, Gaussian signalling in the form of beam-forming is optimal, and no pre-processing of information is necessary.Comment: Submitted to IEEE Transactions on Information Theor

The MIMOME Channel

The MIMOME channel is a Gaussian wiretap channel in which the sender, receiver, and eavesdropper all have multiple antennas. We characterize the secrecy capacity as the saddle-value of a minimax problem. Among other implications, our result establishes that a Gaussian distribution maximizes the secrecy capacity characterization of Csisz{\'a}r and K{\"o}rner when applied to the MIMOME channel. We also determine a necessary and sufficient condition for the secrecy capacity to be zero. Large antenna array analysis of this condition reveals several useful insights into the conditions under which secure communication is possible.Comment: In Proceedings of the 45th Annual Allerton Conference on Communication, Control, and Computing, October 2007, 8 page