State Probing over State-Dependent Additive Gaussian Channels

Abstract

State dependent models have found wide applications in information theory and communications. The major applications include coding for memory with defective cells, MIMO broadcast channels for future wireless networks, etc. In both these models, the state process is available only at the transmitter and not at the receiver. Acquiring the state process at the transmitter often comes with an associated cost. To model this, message dependent actions on whether to acquire the state process was recently proposed in literature. An open question here is whether the performance can be as good by only acquiring part of the state process. In this paper, we demonstrate that there is always a price to be paid if the complete state process is not acquired, settling a known open question. In the process, we also characterize the exact capacity of such state probing models, which was hitherto unknown.