On the Capacity Equivalence with Side Information at Transmitter and Receiver

Abstract— In this paper, a channel that is contaminated by two independent Gaussian noises S ∼ N (0, Q) and Z0 ∼ N (0, N0) is considered. The capacity of this channel is computed when independent noisy versions of S are known to the transmitter and/or receiver. It is shown that the channel capacity is greater then the capacity when S is completely unknown, but is less then the capacity when S is perfectly known at the transmitter or receiver. For example, if there is one noisy version of S known at the transmitter only, the capacity is 1 2 log(1+ P Q(N1/(Q+N1))+N0 ), where P is the input power constraint and N1 is the power of the noise corrupting S. Further, it is shown that the capacity with knowledge of any independent noisy versions of S at the transmitter is equal to the capacity with knowledge of the statistically equivalent noisy versions of S at the receiver. The result is also applied to multiple access channel to show the increase of the capacity region with noisy side information of S.