Secure broadcasting using multiple antennas

We consider three different secure broadcasting scenarios: i) Broadcast channels with common and confidential messages (BCC), ii) multi-receiver wiretap channels with public and confidential messages, and iii) compound wiretap channels. The BCC is a broadcast channel with two users, where in addition to the common message sent to both users, a private message, which needs to be kept hidden as much as possible from the other user, is sent to each user. In this model, each user treats the other user as an eavesdropper. The multi-receiver wiretap channel is a broadcast channel with two legitimate users and an external eavesdropper, where the transmitter sends a pair of public and confidential messages to each legitimate user. Although there is no secrecy concern about the public messages, the confidential messages need to be kept perfectly secret from the eavesdropper. The compound wiretap channel is a compound broadcast channel with a group of legitimate users and a group of eavesdroppers. In this model, the transmitter sends a common confidential message to the legitimate users, and this confidential message needs to be kept perfectly secret from all eavesdroppers. In this paper, we provide a survey of the existing information-theoretic results for these three forms of secure broadcasting problems, with a closer look at the Gaussian multiple-input multiple-output (MIMO) channel models. We also present the existing results for the more general discrete memory-less channel models, as they are often the first step in obtaining the capacity results for the corresponding Gaussian MIMO channel models.