Analyzing linear 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 minentropy rate then the output has min-entropy rate close to . 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 give a refined analysis of the merger constructed by [Raz05] (based on [LRVW03]). Our analysis uses min-entropy instead of Shannon's entropy to derive tighter results than the ones obtained in [Raz05]. We show that for every r it is possible to construct a merger that takes as input k strings of length n bits each, and outputs a string of length n/r bits, such that if one of the input sources has min-entropy b, the output will be close to having min-entropy b/(r + 1). This merger uses a constant number of additional uniform bits when k and r are constants. One advantage of our analysis is ...

• Type: Journal
• Year: 2008
• Where: RSA
• Authors: Zeev Dvir, Ran Raz
• Keywords: Input Sources, Random Source, RSA 2008, Single Random Source