On the Joint Entropy of $d$-Wise-Independent Variables
نویسندگان
چکیده
How low can be the joint entropy of n d-wise independent (for d ≥ 2) discrete random variables? This question has been posed and partially answered in a recent work of Babai [Bab13]. In this paper we improve some of his bounds, prove new bounds in a wider range of parameters and show matching upper bounds in some special cases. In particular, we prove tight lower bounds for the min-entropy (as well as the entropy) of pairwise and three-wise independent balanced binary variables for infinitely many values of n.
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