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- W4296262930 abstract "How low can the joint entropy of $n$ $d$-wise independent (for $dge2$) discrete random variables be, subject to given constraints on the individual distributions (say, no value may be taken by a variable with probability greater than $p$, for $p<1$)? This question has been posed and partially answered in a recent work of Babai. 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 $n$." @default.
- W4296262930 created "2022-09-19" @default.
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- W4296262930 date "2015-03-27" @default.
- W4296262930 modified "2023-10-16" @default.
- W4296262930 title "On the Joint Entropy of $d$-Wise-Independent Variables" @default.
- W4296262930 doi "https://doi.org/10.48550/arxiv.1503.08154" @default.
- W4296262930 hasPublicationYear "2015" @default.
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