Writing on dirty paper (Corresp.)

A channel with output Y = X + S + Z is examined, The state S N (0, QI) and the noise Z N (0, NI) are multivariate Gaussian random variables (I is the identity matrix. ). The input X R^n satisfies the power constraint (l/n) ₈=₁^nX₈^2 P. If S is unknown to both transmitter and receiver then the capacity is 12 (1 + P/ (N + Q) ) nats per channel use. However, if the state S is known to the encoder, the capacity is shown to be C^ =12 (1 + P/N), independent of Q. This is also the capacity of a standard Gaussian channel with signal-to-noise power ratio P/N. Therefore, the state S does not affect the capacity of the channel, even though S is unknown to the receiver. It is shown that the optimal transmitter adapts its signal to the state S rather than attempting to cancel it.