[Colloquium] Guest speaker announcement

[Ponda Barnes]

Guest Speaker
 
Presented by: Toyota Technological Institute at Chicago
 
Speaker: Sergey Yekhanin
Speaker's home page: http://theory.ics.mit.edu/~yekhanin/
 
 
Date: Wednesday, March 28, 2007
Time: 10:00
Location: TTI-C Conference room
 
Title: New Locally Decodable Codes and Private Information Retrieval 
 Schemes
 
 Abstract: A q-query Locally Decodable Code (LDC) is an error-correcting
code that encodes an n-bit message x as a codeword C(x), such that one can
probabilistically recover any bit x_i of the 
 message by querying only q bits of the codeword C(x), even after some
constant fraction of codeword bits has been corrupted.  The goal of LDC
related research is to minimize the length of such codes.
 
 A q-server private information retrieval (PIR) scheme is a an n-bit string
x replicated between q servers while each server individually learns no
information about i.  The goal of PIR related 
 research is to minimize the communication complexity of such schemes.  We
present a novel algebraic approach to LDCs and PIRs and obtain vast
improvements upon the earlier work.  Specifically, given any Mersenne prime
p = 2^t?  1, we design three query LDCs of length Exp(n^{1/t}), for every n.
Based on the largest known Mersenne prime, this translates to a length  of
less than Exp(n^{10^{?7}}), compared to Exp(n^{1/2}) in the  previous
constructions.  We also design 3-server PIR schemes with  communication
complexity of O(n^{10^{?7}})  to access an n-bit  database, compared to the
previous best scheme with complexity  O(n^{1/5.25}).
 
 It has often been conjectured that there are infinitely many Mersenne
primes.  Under this conjecture, our constructions yield three query locally
decodable codes of sub exponential length and three servers private 
 information retrieval schemes with subpolynomial communication complexity.
 
If you have any questions or would like to meet the speaker, please contact
Ponda Barnes at pondabarnes at tti-c.org.
For future TTI-C talks and events, please go to
http://ttic.uchicago.edu/cal/month.php
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