Increasing the output length of zero‐error dispersers

Abstract

Let $\cal{C}$ be a class of probability distributions over a finite set Ω. A function $D : \Omega \mapsto\{0,1\}^{m}$ is a disperser for $\cal{C}$ with entropy threshold $k$ and error $\epsilon$ if for any distribution X in $\cal{C}$ such that X gives positive probability to at least $2^{k}$ elements we have that the distribution $D(X)$ gives positive probability to at least $(1-\epsilon)2^{m}$ 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.

Document Details

Document Type
Pub Defense Publication
Publication Date
Feb 08, 2011
Source ID
10.1002/rsa.20359

Entities

People

  • Ariel Gabizon
  • Ronen Shaltiel

Organizations

  • Defense Advanced Research Projects Agency
  • Israel Science Foundation

Tags

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Image Processing and Computer Vision.
  • Statistical inference.