A Strong Data Processing Inequality for Thinning Poisson Processes and Some Applications

Ligong Wang (1)

1 ETIS - UMR 8051 - Equipes Traitement de l'Information et Systèmes

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.

Domaines: Théorie de l'information [cs.IT]

Ligong Wang. A Strong Data Processing Inequality for Thinning Poisson Processes and Some Applications. International Symposium on Information Theory, Jun 2017, Aachen, Germany. ⟨hal-01556736⟩