Three-user MIMO MACs with cooperation

We study the three-user multi-antenna Gaussian multiple-access channel (MAC) where prior to the transmission over the MAC the transmitters can communicate with each other over noise-free broadcast pipes of given capacities. We present the capacity region of this channel. Additionally, we also study the three-user multi-antenna Gaussian MAC with common messages and present its capacity region. The main step in deriving these two capacity results consists in proving that Gaussian distributions maximize certain mutual information expressions under multiple Markov constraints. Towards this end, a tool previously used is extended to the vector case and to multiple Markov conditions.