Extractors for a constant number of polynomially small min-entropy independent sources

We consider the problem of randomness extraction from independent sources. We construct an extractor that can extract from a constant number of independent sources of length n, each of which have min-entropy n for an arbitrarily small constant > 0. Our result is different from recent work [BIW04, BKS+ 05, Raz05, Bou05] for this problem in the sense that it does not rely on any results from additive number theory. Our extractor is built by composing previous constructions of strong seeded extractors in simple ways. Using Bourgain's extractor [Bou05] as a black box, we obtain a new extractor for 2 independent blockwise sources with few blocks, even when the min-entropy is as small as polylog(n). We also show how to modify the 2 source disperser for linear min-entropy of Barak et al. [BKS+ 05] and the 3 source extractor of Raz [Raz05] to get dispersers/extractors with exponentially small error and linear output length where previously both were constant. In terms of Ramsey Hyper...

• Type: Conference
• Year: 2006
• Where: STOC
• Authors: Anup Rao
• Keywords: Algorithms, Explicit O(1/)-uniform Hypergraphs, Linear Output Length, Source Extractor, STOC 2006