Writing on dirty paper (Corresp.)

Abstract

A channel with outputY = X + S + Zis examined, The stateS \sim N(0, QI)and the noiseZ \sim N(0, NI)are multivariate Gaussian random variables (Iis the identity matrix.). The inputX \in R^{n}satisfies the power constraint(l/n) \sum_{i=1}^{n}X_{i}^{2} \leq P. IfSis unknown to both transmitter and receiver then the capacity is\frac{1}{2} \ln (1 + P/( N + Q))nats per channel use. However, if the stateSis known to the encoder, the capacity is shown to beC^{\ast} =\frac{1}{2} \ln (1 + P/N), independent ofQ. This is also the capacity of a standard Gaussian channel with signal-to-noise power ratioP/N. Therefore, the stateSdoes not affect the capacity of the channel, even thoughSis unknown to the receiver. It is shown that the optimal transmitter adapts its signal to the stateSrather than attempting to cancel it.