TY - JOUR

T1 - Storing information with extractors

AU - Ta-Shma, Amnon

PY - 2002/9/15

Y1 - 2002/9/15

N2 - We deal with the problem of storing a set of K elements that are taken from a large universe of size N, such that membership in the set can be determined with high probability by looking at just one bit of the representation. Buhrman et al. show an explicit construction with about K2 log N storing bits. We show an explicit construction with about K1+o(1) storing bits, that gets closer to the optimal K log N bound. Our technique is of independent interest. Buhrman et al. show a non-explicit optimal (up to constant factors) construction that is based on the existence of certain good unbalanced expanders. To make the construction explicit one needs to be able to explicitly 'encode' and 'decode' such expanding graphs. We generalize the notion of loss-less condensers of Ta-Shma et al. [Proc. 33rd Annual ACM Symposium on Theory of Computing, 2001, pp. 143-152] and build such graphs. We further show how to efficiently decode such graphs using an observation from Ta-Shma and Zuckerman [Manuscript, 2001] about Trevisan's extractor.

AB - We deal with the problem of storing a set of K elements that are taken from a large universe of size N, such that membership in the set can be determined with high probability by looking at just one bit of the representation. Buhrman et al. show an explicit construction with about K2 log N storing bits. We show an explicit construction with about K1+o(1) storing bits, that gets closer to the optimal K log N bound. Our technique is of independent interest. Buhrman et al. show a non-explicit optimal (up to constant factors) construction that is based on the existence of certain good unbalanced expanders. To make the construction explicit one needs to be able to explicitly 'encode' and 'decode' such expanding graphs. We generalize the notion of loss-less condensers of Ta-Shma et al. [Proc. 33rd Annual ACM Symposium on Theory of Computing, 2001, pp. 143-152] and build such graphs. We further show how to efficiently decode such graphs using an observation from Ta-Shma and Zuckerman [Manuscript, 2001] about Trevisan's extractor.

KW - Condensers

KW - Data structures

KW - Expanders

KW - Extractors

KW - List decoding

UR - http://www.scopus.com/inward/record.url?scp=0037105924&partnerID=8YFLogxK

U2 - 10.1016/S0020-0190(02)00206-5

DO - 10.1016/S0020-0190(02)00206-5

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AN - SCOPUS:0037105924

SN - 0020-0190

VL - 83

SP - 267

EP - 274

JO - Information Processing Letters

JF - Information Processing Letters

IS - 5

ER -