Capacity Region of Gaussian MIMO Broadcast Channels with Common and Confidential Messages

We study the two-user Gaussian multiple-input multiple-output (MIMO) broadcast channel with common and confidential messages. In this channel, the transmitter sends a common message to both users, and a confidential message to each user which needs to be kept perfectly secret from the other user. We obtain the entire capacity region of this channel. We also explore the connections between the capacity region we obtain for the Gaussian MIMO broadcast channel with common and confidential messages and the capacity region of its non-confidential counterpart, i.e., the Gaussian MIMO broadcast channel with common and private messages, which is not known completely.

💡 Research Summary

The paper investigates a two‑user Gaussian multiple‑input multiple‑output (MIMO) broadcast channel in which the transmitter simultaneously delivers a common message to both receivers and a confidential message to each receiver that must be kept perfectly secret from the other. The authors derive the exact capacity region of this channel, providing both an achievability scheme and a matching converse.

System model. The transmitter has (t) antennas and sends a vector (\mathbf{X}) subject to an average power constraint (\mathrm{tr}(\mathbb{E}