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2011 26th Annual IEEE Conference on Computational Complexity
Improved Constructions of Three Source Extractors
San Jose, California USA
June 08-June 11
ISBN: 978-0-7695-4411-3
We study the problem of constructing extractors for independent weak random sources. The probabilistic method shows that there exists an extractor for two independent weak random sources on $n$ bits with only logarithmic min-entropy. However, previously the best known explicit two source extractor only achieves min-entropy $0.499n$ \cite{Bourgain05}, and the best known three source extractor only achieves min-entropy $n^{0.9}$ \cite{Rao06}. It is a long standing open problem to construct extractors that work for smaller min-entropy. In this paper we construct an extractor for three independent weak random sources on $n$ bits with min-entropy $n^{1/2+\delta}$, for any constant $0
Index Terms:
randomness, independent, affine, extractor
Citation:
Xin Li, "Improved Constructions of Three Source Extractors," ccc, pp.126-136, 2011 26th Annual IEEE Conference on Computational Complexity, 2011
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