A New Tight Upper Bound on the Entropy of Sums

Abstract

We consider the independent sum of a given random variable with a Gaussian variable and an infinitely divisible one. We find a novel tight upper bound on the entropy of the sum which still holds when the variable possibly has an infinite second moment. The proven bound has several implications on both information theoretic problems and infinitely divisible noise channels’ transmission rates.

Keywords

• entropy of sums
• upper bound
• infinite variance
• infinitely divisible
• differential entropy