 
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
