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Extractors for a Constant Number of Polynomially Small MinEntropy Independent Sources

Summary: Extractors for a Constant Number of Polynomially Small
Min­Entropy Independent Sources
Anup Rao #
Department of Computer Science,
University of Texas at Austin
March 22, 2006
We consider the problem of randomness extraction from independent sources. We construct
an extractor that can extract from a constant number of independent sources of length n, each of
which have min­entropy n # for an arbitrarily small constant # > 0. Our extractor is obtained by
composing seeded extractors in simple ways. We introduce a new technique to condense independent
somewhere­random sources which looks like a useful way to manipulate independent sources. Our
techniques are di#erent from those used in recent work [BIW04, BKS + 05, Raz05, Bou05] for this
problem in the sense that they do not rely on any results from additive number theory.
Using Bourgain's extractor [Bou05] as a black box, we obtain a new extractor for 2 independent
block­sources with few blocks, even when the min­entropy is as small as polylog(n). We also show
how to modify the 2 source disperser for linear min­entropy of Barak et al. [BKS + 05] and the 3
source extractor of Raz [Raz05] to get dispersers/extractors with exponentially small error and
linear output length where previously both were constant.


Source: Anderson, Richard - Department of Computer Science and Engineering, University of Washington at Seattle


Collections: Computer Technologies and Information Sciences