Transmission of common, public and confidential messages in broadcast channels with multiple antennas

We study the Gaussian multiple-input multiple-output (MIMO) wiretap channel, which consists of a transmitter, a legitimate user, and an eavesdropper. In this channel, the transmitter sends a common message to both the legitimate user and the eavesdropper. Moreover, the legitimate user receives a private message, which is desired to be kept hidden as much as possible from the eavesdropper. We obtain the entire capacity-equivocation region of the Gaussian MIMO wiretap channel. This region contains all achievable common message, private message, and private message's equivocation rates. This capacity-equivocation region is equal to the capacity region of a Gaussian MIMO broadcast channel where the transmitter sends a common message to both the legitimate user and the eavesdropper, a public message to the legitimate user on which there is no secrecy constraint, and a confidential message to the legitimate user which needs to kept perfectly secret from the eavesdropper.