Summary: An Exposition of Bourgain's 2­Source Extractor
Anup Rao #
March 28, 2007
Abstract
A construction of Bourgain [Bou05] gave the first 2­source extractor to break the min­entropy
rate 1/2 barrier. In this note, we write an exposition of his result, giving a high level way to view
his extractor construction.
We also include a proof of a generalization of Vazirani's XOR lemma that seems interesting in
its own right, and an argument (due to Boaz Barak) that shows that any two source extractor with
su#ciently small error must be strong.
Keywords: Extractors
# Department of Computer Science, University of Texas at Austin, arao@cs.utexas.edu. Supported in part by an
MCD fellowship from UT Austin and NSF Grant CCR­0310960.

1 Introduction
The min­entropy of a distribution is k if
max
x#Supp(X)
Pr[X = x] = 2 -k
We say that a function Ext : {0, 1} n

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

Collections: Computer Technologies and Information Sciences