Analyzing linear mergers

نویسندگان

  • Zeev Dvir
  • Ran Raz
چکیده

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 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 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 that b (the min-entropy of the ’good’ source ) can be as small as a constant, while in the analysis given in [Raz05], b is required to be linear in n.

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عنوان ژورنال:
  • Electronic Colloquium on Computational Complexity (ECCC)

دوره   شماره 

صفحات  -

تاریخ انتشار 2005