State Amplification

TL;DR

This paper characterizes the optimal tradeoff between data transmission rate and the amount of channel state information learned at the receiver, considering causal and noncausal state information at the sender.

Contribution

It provides a theoretical framework for the tradeoff between communication rate and state information conveyance in state-dependent channels.

Findings

Derived the capacity-rate tradeoff for causal and noncausal cases.

Connected the results to dual problems of state masking.

Established a fundamental limit on state information transmission.

Abstract

We consider the problem of transmitting data at rate R over a state dependent channel p(y|x,s) with the 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. 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.