Capacity Theorems for Channels with Designable Feedback

Finite-rate, or limited, channel state feedback from receivers to transmitters may provide significant information rate gain. We provide capacities for single-user and multiuser (multiple access) channels with designable finite rate channel state feedback and input constraints. Cases of finite input/output/state alphabets, spaces with probability density functions, and Multiple-Input Multiple-Output (MIMO) fading channels are considered. It is shown that the optimal feedback is memoryless and is a function of the current channel state only. The optimal input function is also memoryless and depends on current feedback only. The key result is that the optimal feedback and transmission strategies may be time varying and for the single user case, deterministic feedback is optimal and the capacity is maximum of mutual information plus a duality gap, which may be strictly positive. Moreover, random feedback may outperform time invariant deterministic feedback.