Two Measures of Dependence

Amos Lapidoth, Christoph Pfister

Published 2016-07-08Version 1

Motivated by a distributed task-encoding problem, two closely related families of dependence measures are introduced. They are based on the R\'enyi divergence of order {\alpha} and the relative {\alpha}-entropy, respectively, and both reduce to the mutual information when the parameter {\alpha} is one. Their properties are studied and it is shown that the first measure shares many properties with mutual information, including the data-processing inequality. The second measure does not satisfy the data-processing inequality, but it appears naturally in the context of distributed task encoding.