The Capacity of Less Noisy Cognitive Interference Channels

Fundamental limits of the cognitive interference channel (CIC) with two pairs of transmitter-receiver has been under exploration for several years. In this paper, we study the discrete memoryless cognitive interference channel (DM-CIC) in which the cognitive transmitter non-causally knows the message of the primary transmitter. The capacity of this channel is not known in general; it is only known in some special cases. Inspired by the concept of less noisy broadcast channel (BC), in this work we introduce the notion of less noisy cognitive interference channel. Unlike BC, due to the inherent asymmetry of the cognitive channel, two different less noisy channels are distinguishable; these are named the primary-less-noisy and cognitive-less-noisy channels. We derive capacity region for the latter case, by introducing inner and outer bounds on the capacity of the DM-CIC and showing that these bounds coincide for the cognitive-less-noisy channel. Having established the capacity region, we prove that superposition coding is the optimal encoding technique.