Optimal Power Allocation for Parallel Gaussian Broadcast Channels with Independent and Common Information

We consider a set of parallel, two-user 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 has been implicitly characterized in the past, but we provide an explicit characterization of the power and rate allocation schemes that achieve the boundary of the three-dimensional rate region. Unlike the broadcast channel with only independent information, we find that the optimal power allocation policy cannot be viewed as a generalization of single-user water-filling. We also consider MIMO broadcast channels, which are non-degraded in general. We propose an achievable region based on dirty paper coding, and discuss the maximum common information rate achievable over these channels.