Information Theoretic Exemplification of the Receiver Re-cognition and a More General Version for the Costa Theorem

In this paper, we study the impact of receiver cognition on the channel capacity information theoretically. As a new idea, we consider the receiver cognition as side information known at the receiver correlated to the channel noise and we derive a capacity theorem based on the Gaussian version of the Cover-Chiang capacity theorem for two-sided state information channel. As intuitively expected, the receiver cognition increases the channel capacity and our theorem shows this increase quantitatively. Also, our theorem, while including the famous Costa theorem as its special case, shows the impact of the correlation between the channel input and the side information known at the transmitter on the channel capacity.