Thumbnail
Access Restriction
Subscribed

Author Guruswami, Venkatesan ♦ Umans, Christopher ♦ Vadhan, Salil
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©2009
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Expander graphs ♦ Condensers ♦ Error-correcting codes ♦ List decoding ♦ Randomness extractors
Abstract We give an improved explicit construction of highly unbalanced bipartite expander graphs with expansion arbitrarily close to the degree (which is polylogarithmic in the number of vertices). Both the degree and the number of right-hand vertices are polynomially close to optimal, whereas the previous constructions of Ta-Shma et al. [2007] required at least one of these to be quasipolynomial in the optimal. Our expanders have a short and self-contained description and analysis, based on the ideas underlying the recent list-decodable error-correcting codes of Parvaresh and Vardy [2005]. Our expanders can be interpreted as near-optimal “randomness condensers,” that reduce the task of extracting randomness from sources of arbitrary min-entropy rate to extracting randomness from sources of min-entropy rate arbitrarily close to 1, which is a much easier task. Using this connection, we obtain a new, self-contained construction of randomness extractors that is optimal up to constant factors, while being much simpler than the previous construction of Lu et al. [2003] and improving upon it when the error parameter is small (e.g., 1/poly(n)).
ISSN 00045411
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2009-07-02
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 56
Issue Number 4
Page Count 34
Starting Page 1
Ending Page 34


Open content in new tab

   Open content in new tab
Source: ACM Digital Library