Information theoretic inequalities

The role of inequalities in information theory is reviewed, and the relationship of these inequalities to inequalities in other branches of mathematics is developed. The simple inequalities for differential entropy are applied to the standard multivariate normal to furnish new and simpler proofs of the major determinant inequalities in classical mathematics. The authors discuss differential entropy inequalities for random subsets of samples. These inequalities when specialized to multivariate normal variables provide the determinant inequalities that are presented. The authors focus on the entropy power inequality (including the related Brunn-Minkowski, Young´s, and Fisher information inequalities) and address various uncertainty principles and their interrelations