On extracting randomness from weak random sources (extended abstract)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Extractors: optimal up to constant factors
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Extracting Randomness Using Few Independent Sources
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Extractors with weak random seeds
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
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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 δ then the output has min-entropy rate close to δ. 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 [6]. Our analysis shows that the min-entropy rate of this merger's output is actually 0.52δ instead of 0.5δ, where δ 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 [6] and introduce a new technique that involves results from additive number theory.