On the entropy and mutual information of point processes

This paper is focused on information theoretic properties of point processes. Firstly, we discuss the entropy of a point process and the entropy rate of a stationary point process. Then we give explicit formulas for these quantities in the Poisson case, as well as maximal entropy properties for homogeneous Poisson point processes. Secondly, we define the mutual information rate of two stationary point processes. We then give explicit formulas for the mutual information rate between a homogeneous Poisson point process and its displacement.