 
Summary: Extractors for a Constant Number of Polynomially Small
MinEntropy Independent Sources
Anup Rao #
Department of Computer Science,
University of Texas at Austin
arao@cs.utexas.edu
March 22, 2006
Abstract
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.
