Capacity region and optimum power control strategies for fading Gaussian multiple access channels with common data

A Gaussian multiple access channel (MAC) with common data is considered. Capacity region when there is no fading is known in an implicit form. We provide an explicit characterization of the capacity region and provide a simpler encoding/decoding scheme than that mentioned in work by Slepian and Wolf. Next, we give a characterization of the ergodic capacity region when there is fading, and both the transmitters and the receiver know the channel perfectly. Then, we characterize the optimum power allocation schemes that achieve arbitrary rate tuples on the boundary of the capacity region. Finally, we provide an iterative method for the numerical computation of the ergodic capacity region and the optimum power control strategies.