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TR05-067 | 28th June 2005 00:00

An Improved Analysis of Mergers


Authors: Zeev Dvir, Amir Shpilka
Publication: 5th July 2005 13:29
Downloads: 1395


Mergers are functions that transform k (possibly dependent) random sources into a single random source, in a way that ensures that if one of the input sources has min-entropy rate $\delta$ then the output has min-entropy rate close to $\delta$. Mergers have proven to be a very useful tool in explicit constructions of extractors and condensers, and are also interesting objects in their own right. In this work we present a new analysis of the merger construction of [LRVW03]. Our analysis shows that the min-entropy rate of this merger's output is actually $0.52*\delta$ instead of $0.5*\delta$, where $\delta$ is the min-entropy rate of one of the inputs. To obtain this result we deviate from the usual linear algebra methods that were used by [LRVW03] and introduce a new technique that involves results from additive number theory.

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