On the Capacity Equivalence with Side Information at Transmitter and Receiver

Details On the Capacity Equivalence with Side Information at Transmitter and Receiver On the Capacity Equivalence with Side Information at Transmitter and Receiver

2008-06-16

arxiv.org/abs/0806.2643v2

Computer Science

Information Theory

5 pages in IEEE 2 column format, submitted to IEEE Trans. Information Theory in June, 2008

Scientific paper

In this paper, a channel that is contaminated by two independent Gaussian noises $S ~ N(0,Q)$ and $Z_0 ~ N(0,N_0)$ 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 $0.5\log(1+\frac{P}{Q(N_1/(Q+N_1))+N_0})$, where $P$ is the input power constraint and $N_1$ 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.

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