Extracting Randomness via Repeated Condensing (2000)
| Venue: | In Proceedings of the 41st Annual IEEE Symposium on Foundations of Computer Science |
| Citations: | 39 - 16 self |
BibTeX
@INPROCEEDINGS{Reingold00extractingrandomness,
author = {Omer Reingold and Ronen Shaltiel and Avi Wigderson},
title = {Extracting Randomness via Repeated Condensing},
booktitle = {In Proceedings of the 41st Annual IEEE Symposium on Foundations of Computer Science},
year = {2000},
pages = {22--31}
}
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Abstract
On an input probability distribution with some (min-)entropy an extractor outputs a distribution with a (near) maximum entropy rate (namely the uniform distribution). A natural weakening of this concept is a condenser, whose output distribution has a higher entropy rate than the input distribution (without losing much of the initial entropy). In this paper we construct efficient explicit condensers. The condenser constructions combine (variants or more efficient versions of) ideas from several works, including the block extraction scheme of [NZ96], the observation made in [SZ94, NT99] that a failure of the block extraction scheme is also useful, the recursive "win-win" case analysis of [ISW99, ISW00], and the error correction of random sources used in [Tre99]. As a natural byproduct, (via repeated iterating of condensers), we obtain new extractor constructions. The new extractors give significant qualitative improvements over previous ones for sources of arbitrary min-entropy; they...
