An Improved Analysis of Mergers

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 [LRVW03]. Our analysis shows that the min-entropy rate of this merger’s output is actually 0.52 · δ instead of 0.5 · δ, 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 [LRVW03] and introduce a new technique that involves results from additive number theory.