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Summary: Extractors for Three Uneven-Length Sources
Anup Rao,1
and David Zuckerman,2
1
School of Mathematics, Institute for Advanced Study
arao@ias.edu
2
Department of Computer Science, University of Texas at Austin
diz@cs.utexas.edu
Abstract. We construct an efficient 3-source extractor that requires one of the sources to be signif-
icantly shorter than the min-entropy of the other two sources. Our extractors work even when the
longer, n-bit sources have min-entropy n(1)
and the shorter source has min-entropy log10
n. Previous
constructions for independent sources with min-entropy n
required (1/) sources [Rao06]. Our con-
struction relies on lossless condensers [GUV07] based on Parvaresh-Vardy codes [PV05], as well as on
a 2-source extractor for a block source and general source [BRSW06].
1 Introduction
Motivated by the widespread use of randomness in computer science, researchers have sought algorithms
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