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A New Tight Upper Bound on the Entropy of Sums
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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.
Title: A New Tight Upper Bound on the Entropy of Sums
Description:
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.
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