2012 IEEE 27th Conference on Computational Complexity (2011)

San Jose, California USA

June 8, 2011 to June 11, 2011

ISSN: 1093-0159

ISBN: 978-0-7695-4411-3

pp: 126-136

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/CCC.2011.26

ABSTRACT

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",

*2012 IEEE 27th Conference on Computational Complexity*, vol. 00, no. , pp. 126-136, 2011, doi:10.1109/CCC.2011.26