Capacity of time-varying channels with channel side information at the sender and receiver

The capacity of time-varying asymptotically block memoryless channels with causal channel side information at the sender and receiver is considered. We present a formal weak coding theorem and its converse. We then show that our coding theorem can be used to obtain the capacity of time-varying ISI channels, which cannot generally be considered using traditional decomposition methods. For perfect instantaneous side information, the form of the input distribution that maximizes capacity is found to be conditional Gaussian. We also consider the capacity of flat fading channels with imperfect channel estimates