Multiple Access Channel with Partial and Controlled Cribbing Encoders

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In this paper we consider a multiple access channel (MAC) with partial cribbing encoders. This means that each of two encoders obtains a deterministic function of the other encoder output with or without delay. The partial cribbing scheme 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 the 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 functions 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.