A new entropy power inequality
IEEE Transactions on Information Theory
Ultra logconcave sequences and negative dependence
Journal of Combinatorial Theory Series A
Concavity of entropy under thinning
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
Monotonic convergence in an information-theoretic law of small numbers
IEEE Transactions on Information Theory
Thinning, entropy, and the law of thin numbers
IEEE Transactions on Information Theory
A simple proof of the entropy-power inequality
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Generalized Entropy Power Inequalities and Monotonicity Properties of Information
IEEE Transactions on Information Theory
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We consider the entropy of sums of independent discrete random variables, in analogy with Shannon's Entropy Power Inequality, where equality holds for normals. In our case, infinite divisibility suggests that equality should hold for Poisson variables. We show that some natural analogues of the EPI do not in fact hold, but propose an alternative formulation which does always hold. The key to many proofs of Shannon's EPI is the behavior of entropy on scaling of continuous random variables. We believe that Rényi's operation of thinning discrete random variables plays a similar role to scaling, and give a sharp bound on how the entropy of ultra log-concave random variables behaves on thinning. In the spirit of the monotonicity results established by Artstein, Ball, Barthe, and Naor, we prove a stronger version of concavity of entropy, which implies a strengthened form of our discrete EPI.