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In this paper, the authors first consider a channel that is contaminated by two independent Gaussian noises S ~ N(0,Q) and Z0 ~ N(0,N0). 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 than the capacity when S is completely unknown, but is less than 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.
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