2012 IEEE 27th Conference on Computational Complexity (2012)

Porto Portugal

June 26, 2012 to June 29, 2012

ISSN: 1093-0159

ISBN: 978-0-7695-4708-4

pp: 309-315

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/CCC.2012.25

ABSTRACT

We give a new construction of condensers based on Parvaresh-Vardy codes [PV]. Our condensers have entropy rate $(1 - \alpha)$ for sub constant $\alpha$ (in contrast to [GUV] which required constant $\alpha$) and suffer only sub linear entropy loss. Known extractors can be applied to the output to extract all but a sub constant fraction of the minentropy. The resulting $(k, \eps)$ extractor $E:{0, 1}^n \times {0, 1}^d \right arrow {0, 1}^m$ has output length $m = (1 - \alpha)k$ with $\alpha = 1/\poly\log(n)$, and seed length $d = O(\log n)$, when $\eps \ge 1/2^{\log^\beta n}$ for any constant $\beta

INDEX TERMS

condensers, randomness extractors, Parvaresh-Vardy codes

CITATION

"Better Condensers and New Extractors from Parvaresh-Vardy Codes",

*2012 IEEE 27th Conference on Computational Complexity*, vol. 00, no. , pp. 309-315, 2012, doi:10.1109/CCC.2012.25