On the joint entropy of $d$-wise-independent variables
نویسندگان
چکیده
منابع مشابه
On the Joint Entropy of $d$-Wise-Independent Variables
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 ...
متن کاملAlmost k-wise Independent Variables
We will now consider the problem of creating a set of bitstrings such that the bits are almost k-wise independent. Our method consists of two steps. In the first step we create a set of bitstrings such that parity on every fixed index set is almost even. In the second step we present a method to convert such a set into a set where the bits are almost k-wise independent. For presentational reaso...
متن کاملOn Construction of k-Wise Independent Random Variables
A 0-1 probability space is a probability space ((; 2 ; P), where the sample space f0;1g n for some n. A probability space is k-wise independent if, when Yi is deened to be the ith coordinate of the random n-vector, then any subset of k of the Yi's is (mutually) independent, and it is said to be a probability space for p1; p2; :::;pn if PYi = 1] = pi. We study constructions of k-wise independent...
متن کاملSimple Constructions of Almost k-Wise Independent Random Variables
We present three alternative simple constructions of small proba. bility spaces on n bits for which any k bits are almost independent. The number of bits used to specify a point in the sample space is (2 +o(l»(loglog n + log k + log ~), where f is the statistical difference between the distribution induced on any k bit locations and the uni form distribution. This is asymptotically comparable...
متن کاملA Simple Construction of Almost k-wise Independent Random Variables
We present a simple construction of a small probability space on n bits for which any k bits are almost independent. The number of bits used to specify a point in the sample space is O(log log n + k + log ~), where e is the statistical difference between of the distribution induced on any k bit locations and the uniform distribution. This is asymptotically comparable to the construction recentl...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Commentationes Mathematicae Universitatis Carolinae
سال: 2016
ISSN: 0010-2628,1213-7243
DOI: 10.14712/1213-7243.2015.169