Zero-Fixing Extractors for Sub-Logarithmic Entropy

@inproceedings{Cohen2014ZeroFixingEF,
  title={Zero-Fixing Extractors for Sub-Logarithmic Entropy},
  author={Gil Cohen and Igor Shinkar},
  booktitle={Electronic Colloquium on Computational Complexity},
  year={2014}
}
An (n, k)-bit-fixing source is a distribution on n bit strings, that is fixed on n − k of the coordinates, and jointly uniform on the remaining k bits. Explicit constructions of bit-fixing extractors by Gabizon, Raz and Shaltiel [SICOMP 2006] and Rao [CCC 2009], extract (1 − o(1)) · k bits for k = poly log n, almost matching the probabilistic argument. Intriguingly, unlike other well-studied sources of randomness, a result of Kamp and Zuckerman [SICOMP 2006] shows that, for any k, some small… CONTINUE READING

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