Multiple access channel with partial and controlled cribbing encoders

In this paper we consider the multiple access channel (MAC) with partial cribbing encoders which means that each encoder obtains a deterministic function of the other encoder output, possibly with delay. The partial cribbing is especially motivated by the additive noise Gaussian MAC since perfect cribbing results in the degenerated case of full cooperation between the encoders and requires an infinite entropy link. We derive a single letter characterization of the capacity of MAC with partial cribbing for the cases of causal and strictly causal partial cribbing. Several numerical examples such as quantized cribbing are presented.We further consider and derive the capacity region where the cribbing depends on actions that are function of the previous cribbed observations. In particular, we consider a scenario where the action is “to crib or not to crib” and show that a naive time-sharing strategy is not optimal.