Gaussian channels with state

Channel capacity and state estimation for state-dependent Gaussian channels

Arak Sutivong, Mung Chiang, Thomas M. Cover, and Young-Han Kim

We formulate a problem of state information transmission over a state-dependent channel with states known at the transmitter. In particular, we solve a problem of minimizing the mean-squared channel state estimation error E||S^n - hat S^n|| for a state-dependent additive Gaussian channel Y^n = X^n + S^n + Z^n with an independent and identically distributed (i.i.d.) Gaussian state sequence S^n = (S_1, ldots, S_n) known at the transmitter and an unknown i.i.d. additive Gaussian noise Z^n. We show that a simple technique of direct state amplification (i.e., X^n = alpha S^n), where the transmitter uses its entire power budget to amplify the channel state, yields the minimum mean-squared state estimation error. This same channel can also be used to send additional independent information at the expense of a higher channel state estimation error. We characterize the optimal tradeoff between the rate R of the independent information that can be reliably transmitted and the mean-squared state estimation error D. We show that any optimal (R, D) tradeoff pair can be achieved via a simple power-sharing technique, whereby the transmitter power is appropriately allocated between pure information transmission and state amplification.