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A channel with output is examined, The state and the noise are multivariate Gaussian random variables ( is the identity matrix.). The input satisfies the power constraint . If is unknown to both transmitter and receiver then the capacity is nats per channel use. However, if the state is known to the encoder, the capacity is shown to be , independent of . This is also the capacity of a standard Gaussian channel with signal-to-noise power ratio . Therefore, the state does not affect the capacity of the channel, even though is unknown to the receiver. It is shown that the optimal transmitter adapts its signal to the state rather than attempting to cancel it.