Capacity and dirty paper coding for Gaussian broadcast channels with common information

We consider a set of parallel, two-user scalar Gaussian broadcast channels, where the transmitter wishes to send independent information to each of the receivers and common information to both receivers. The capacity region of this channel is implicitly characterized in [A. El Gamal, (1980)]. Here, we provide an explicit characterization of the power and rate allocation schemes that achieve the boundary of the three-dimensional rate region. We also propose a dirty-paper coding achievable region for MIMO broadcast channels with common information.