An entropy inequality for symmetric random variables.

Jing Hao
Jing Hao

ISIT, (2018): 1600-1604

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Abstract:

We establish a lower bound on the entropy of weighted sums of (possibly dependent) random variables (X 1 , X 2 , …, X n) possessing a symmetric joint distribution. Our lower bound is in terms of the joint entropy of (X 1 , X 2 , …, Xn). We show that for $n$ ≥ 3, the lower bound is tight if and only if X i u0027S are i.i.d. Gaussian rand...More

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