  In this paper, a new and general version of Gaussian channel in presence of
two-sided state information correlated to the channel input and noise is
considered. Determining a general achievable rate for the channel and obtaining
the capacity in a non-limiting case, we try to analyze and solve the Gaussian
version of the Cover-Chiang theorem -as an open problem- mathematically and
information-theoretically. Our capacity theorem, while including all previous
theorems as its special cases, explains situations that can not be analyzed by
them; for example, the effect of the correlation between the side information
and the channel input on the capacity of the channel that can not be analyzed
with Costa's "writing on dirty paper" theorem. Meanwhile, we try to introduce
our new idea, i.e., describing the concept of "cognition" of a communicating
object (transmitter, receiver, relay and so on) on some variable (channel
noise, interference and so on) with the information-theoretic concept of "side
information" correlated to that variable and known by the object. According to
our theorem, the channel capacity is an increasing function of the mutual
information of the side information and the channel noise. Therefore our
channel and its capacity theorem exemplify the "cognition" of the transmitter
and receiver on the channel noise based on the new description. Our capacity
theorem has interesting interpretations originated from this new idea.
