Extracting All the Randomness from a Weakly Random Source

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Extracting All the Randomness from a Weakly Random Source
In this paper, we give two explicit constructions of extractors, both of which work for a source of any min-entropy on strings of length n. The rst extracts any constant fraction of the min-entropy using Olog2 n additional random bits. The second extracts all the min-entropy using Olog3 n additional random bits. Both constructions use fewer truly random bits than any previous construction which works for all min-entropies and extracts a constant fraction of the min-entropy. The extractors are obtained by observing that a weaker notion of combinatorial design" su ces for the Nisan Wigderson pseudorandom generator NW94 , which underlies the recent extractor of Trevisan Tre98 . We give near-optimal constructions of such weak designs" which achieve much better parameters than possible with the notion of designs used by Nisan Wigderson and Trevisan.
Salil P. Vadhan
Added 22 Dec 2010
Updated 22 Dec 2010
Type Journal
Year 1998
Where ECCC
Authors Salil P. Vadhan
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