New Independent Source Extractors with Exponential Improvement

Computer Science/Discrete Mathematics Seminar I
Topic:New Independent Source Extractors with Exponential Improvement
Speaker:Xin Li
Affiliation:University of Washington
Date:Monday, January 28
Time/Room:11:15am - 12:15pm/S-101
Video Link:https://video.ias.edu/1213/csdm/0128-XinLi

We study the problem of constructing extractors for independent weak random sources. The probabilistic method shows that such an extractor exists for two sources on n bits with min-entropy k >= 2 log n. On the other hand, explicit constructions are far from optimal. Previously the best known extractor for (n,k) sources requires O(log n/log k) independent sources [Rao06, Barak-Rao-Shaltiel-Wigderson06]. In this talk I will give a new extractor that uses only O(log (log n/log k))+O(1) independent sources. This improves the previous best result exponentially. The extractor is based on a new method for condensing somewhere random sources, which seems promising for further improvements.