Capacities of time-varying multiple-access channels with side information

We determine the capacity regions for a class of time-varying multiple-access channels (TVMACs), when the underlying channel state evolves in time according to a probability law which is known to the transmitters and the receiver. Additionally, the transmitters and the receiver have access to varying degrees of channel state information (CSI) concerning the condition of the channel. Discrete-time channels with finite input, output and state alphabets are considered first. Next, in order to reduce transmitter complexity, we restrict the encoders at each time instant to depend only on a limited extent of CSI. As a special case, we consider a memoryless TVMAC, with the channel state process being a time-invariant, indecomposable, aperiodic Markov chain. We then study a time-varying (multiple-access) fading channel (TVFC) with additive Gaussian noise, when various amounts of CSI are provided to the transmitters while perfect CSI is available to the receiver, and the fades are assumed to be stationary and ergodic.