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In this paper the study of the cognitive interference channel with a commonmessage, a variation of the classical cognitive interference channel in whichthe cognitive message is decoded at both receivers. We derive the capacity forthe semideterministic channel in which the output at the cognitive decoder is adeterministic function of the channel inputs. We also show capacity to within aconstant gap and a constant factor for the Gaussian channel in which theoutputs are linear combinations of the channel inputs plus an additive Gaussiannoise term. Most of these results are shown using an interesting transmissionscheme in which the cognitive message, decoded at both receivers, is alsopre-coded against the interference experienced at the cognitive decoder. Thepre-coding of the cognitive message does not allow the primary decoder toreconstruct the interfering signal. The cognitive message acts instead as aside information at the primary receiver when decoding its intended message.

The Capacity of the Semi-Deterministic Cognitive Interference Channel with a Common Cognitive Message and Approximate Capacity for the Gaussian Case