Multiple-Access Channel With Partial and Controlled Cribbing Encoders

In this paper, we consider a multiple-access channel (MAC) with partial cribbing encoders. This means that each of the two encoders obtains a deterministic function of the output of the other encoder with or without delay. The partial cribbing scheme is especially motivated by the additive noise Gaussian MAC, where 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 cribbing. Several numerical examples, such as those of 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 taken to decide "to crib or not to crib" and show that a naive time-sharing strategy is not optimal.