An Exposition of Bourgain's 2-Source Extractor

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.