Increasing the Output Length of Zero-Error Dispersers

Let C be a class of probability distributions over a finite set . A function D : {0, 1}m is a disperser for C with entropy threshold k and error if for any distribution X in C such that X gives positive probability to at least 2k elements we have that the distribution D(X) gives positive probability to at least (1 - )2m elements. A long line of research is devoted to giving explicit (that is polynomial time computable) dispersers (and related objects called "extractors") for various classes of distributions while trying to maximize m as a function of k. For several interesting classes of distributions there are explicit constructions in the literature of zero-error dispersers with "small" output length m. In this paper we develop a general technique to improve the output length of zero-error dispersers. This strategy works for several classes of sources and is inspired by a transformation that improves the output length of extractors (which was given in [32] buil...

• Type: Conference
• Year: 2008
• Where: APPROX
• Authors: Ariel Gabizon, Ronen Shaltiel
• Keywords: Algorithms, APPROX 2008, Explicit Constructions, Output Length, Zero-error Dispersers