Distortion-transmission trade-off in real-time transmission of Gauss-Markov sources

The problem of optimal real-time transmission of a Gauss-Markov source under constraints on the expected number of transmissions is considered. This setup is motivated by applications where transmission is sporadic and the cost of switching on the radio and transmitting is significantly more important than the size of the transmitted data packet. The structure of optimal transmission and estimation strategies had been established in the literature. We use these structural results to determine the distortion-transmission function, i.e., the minimum expected distortion that can be achieved when the expected number of transmissions is less than or equal to a particular value. We characterize how the distortion-transmission function scales with the variance of the source and show that it can be computed numerically by solving two Fredholm integral equations of the second kind.