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

We investigate remote estimation over a Gilbert-Elliot channel with feedback. The channel is modelled as an ON/OFF channel, where the state of the channel evolves as a Markov chain. The channel state is observed by the receiver and fed back to the transmitter with one unit delay. In addition, the transmitter gets ACK/NACK feedback for successful/unsuccessful transmission. Using ideas from team theory, we establish the structure of optimal transmission and estimation strategies and identify a dynamic program to determine optimal strategies with that structure. We then consider first-order autoregressive sources where the noise process has unimodal and symmetric distribution. Using ideas from majorization theory, we show that the optimal transmission strategy has a threshold structure and the optimal estimation strategy is Kalman-filter like.