A New Capacity Theorem for the Gaussian Channel with Two-sided Input and Noise Dependent State Information

Gaussian interference known at the transmitter can be fully canceled in a Gaussian communication channel employing dirty paper coding, as Costa shows, when interference is independent of the channel noise and when the channel input designed independently of the interference. In this paper, a new and general version of the 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 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 exemplify the concept of “cognition" of the transmitter or the receiver on a variable (here, the channel noise) with the information-theoretic concept of “side information" correlated to that variable and known at the transmitter or at the receiver. According to our theorem, the channel capacity is an increasing function of the mutual information of the side information and the channel noise.