State amplification

We consider the problem of transmitting data at rate R over a state-dependent channel p (y vertical bar x, s) with state information available at the sender and at the same time conveying the information about the channel state itself to the receiver. The amount of state information that can be learned at the receiver is captured by the mutual information I(S-n; Y-n) between the state sequence S-n and the channel output Y-n. The optimal tradeoff is characterized between the information transmission rate R and the state uncertainty reduction rate Delta, when the state information is either causally or noncausally available at the sender. In particular, when state transmission is the only goal, the maximum uncertainty reduction rate is given by Delta* = max(p(x vertical bar s)) I(X S; Y). This result is closely related and in a sense dual to a recent study by Merhav and Shamai, which solves the problem of masking the state information from the receiver rather than conveying it.