  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.
