Information transfer and its control in linear discrete stochastic systems

Abstract

Information transfer is defined as a measure of the causal inferences between dynamical events. We quantify information transfers and study their responses to interventions or external signals within components of linear discrete stochastic systems. To quantify the causal inferences, we find the difference between the rate of change in the differential entropy of a marginal measure at a given coordinate in the presence and absence of another fixed coordinate. We also integrate theories from optimal control and information theory to compute control signals that result in desired information transfers within the dynamical components. To optimally steer the information transfer to the desired value, we convert the control problem into a nonlinear program, which can be solved numerically. We illustrate our theory with an example of a wireless communication system consisting of various transmitters and receivers. In particular, given a well-defined transmission channel model and the noise, we show that the signal-to-interference-plus-noise ratio, SINR of a receiver due to interference from various transmitters is a function of information transfers to the receiver from the transmitters, and controlling these transfers to desired values aligns with controlling the SINR experienced by the receiver.