State amplification

Abstract—We consider the problem of transmitting data at rate over a state-dependent channel with state information available at the sender and at the same time conveying the infor-mation 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 between the state sequence and the channel output . The optimal tradeoff is charac-terized between the information transmission rate and the state uncertainty reduction rate, 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 re-duction rate is given by . 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. Index Terms—Capacity, causal state information, channels with state information, joint source–channel coding, noncausal state in-formation, state amplification, state uncertainty reduction, writing on dirty paper. I