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We investigate remote estimation over a Gilbert-Elliot channel with feedback.We assume that the channel state is observed by the receiver and fed back tothe transmitter with one unit delay. In addition, the transmitter gets ACK/NACKfeedback for successful/unsuccessful transmission. Using ideas from teamtheory, we establish the structure of optimal transmission and estimationstrategies and identify a dynamic program to determine optimal strategies withthat structure. We then consider first-order autoregressive sources where thenoise process has unimodal and symmetric distribution. Using ideas frommajorization theory, we show that the optimal transmission strategy has athreshold structure and the optimal estimation strategy is Kalman-like.

Structure of optimal strategies for remote estimation over Gilbert-Elliott channel with feedback