 
Summary: Extractors for Three UnevenLength 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 3source extractor that requires one of the sources to be signif
icantly shorter than the minentropy of the other two sources. Our extractors work even when the
longer, nbit sources have minentropy n(1)
and the shorter source has minentropy log10
n. Previous
constructions for independent sources with minentropy n
required (1/) sources [Rao06]. Our con
struction relies on lossless condensers [GUV07] based on ParvareshVardy codes [PV05], as well as on
a 2source 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
