On the Capacity Equivalence with Side Information at Transmitter and Receiver

TL;DR

This paper analyzes the capacity of a Gaussian noise channel with side information about a contaminating noise source at the transmitter and receiver, revealing how partial knowledge affects capacity.

Contribution

It derives the capacity formulas for channels with noisy side information at transmitter and receiver, showing their equivalence and quantifying capacity gains over no side information.

Findings

Capacity increases with side information but remains below perfect knowledge.

Capacity with noisy side information at transmitter equals that at receiver for equivalent noise.

Explicit capacity formula provided for the case of noisy side information at transmitter.

Abstract

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.