A strong data processing inequality for thinning poisson processes and some applications

Abstract

This paper derives a simple strong data processing inequality (DPI) for Poisson processes: after a Poisson process is passed through p-thinning — in which every arrival remains in the process with probability p and is erased otherwise, independently of the other points — the mutual information between the Poisson process and any other random variable is reduced to no more than p times its original value. This strong DPI is applied to prove tight converse bounds in several problems: a hypothesis test with communication constraints, a mutual information game, and a CEO problem.