| | |
Summary: An Exposition of Bourgain's 2-Source Extractor
Anup Rao
March 28, 2007
Abstract
A construction of Bourgain [Bou05] gave the first 2-source extractor to break the min-entropy
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
sufficiently 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 CCR-0310960.
1 Introduction
The min-entropy of a distribution is k if
max
xSupp(X)
Pr[X = x] = 2-k
We say that a function Ext : {0, 1}n × {0, 1}n {0, 1}m is a 2-source extractor for entropy k if
|
