Lower bounds for approximate LDCs

Jop Briët, Zeev Dvir, Guangda Hu, Shubhangi Saraf

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We study an approximate version of q-query LDCs (Locally Decodable Codes) over the real numbers and prove lower bounds on the encoding length of such codes. A q-query (α,δ)-approximate LDC is a set V of n points in ℝd so that, for each i ∈ [d] there are Ω(δn) disjoint q-tuples (u1,...,uq) in V so that span(u 1,...,uq) contains a unit vector whose i'th coordinate is at least α. We prove exponential lower bounds of the form n ≥ 2 Ω(αδ√d) for the case q = 2 and, in some cases, stronger bounds (exponential in d).

Original languageEnglish (US)
Title of host publicationAutomata, Languages, and Programming - 41st International Colloquium, ICALP 2014, Proceedings
PublisherSpringer Verlag
Pages259-270
Number of pages12
EditionPART 1
ISBN (Print)9783662439470
DOIs
StatePublished - Jan 1 2014
Event41st International Colloquium on Automata, Languages, and Programming, ICALP 2014 - Copenhagen, Denmark
Duration: Jul 8 2014Jul 11 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 1
Volume8572 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other41st International Colloquium on Automata, Languages, and Programming, ICALP 2014
CountryDenmark
CityCopenhagen
Period7/8/147/11/14

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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