Locally testable codes with constant rate, distance, and locality

Irit Dinur, Shai Evra, Ron Livne, Alexander Lubotzky, Shahar Mozes

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

13 Scopus citations

Abstract

A locally testable code (LTC) is an error correcting code that has a property-tester. The tester reads q bits that are randomly chosen, and rejects words with probability proportional to their distance from the code. The parameter q is called the locality of the tester. LTCs were initially studied as important components of probabilistically checkable proofs (PCP), and since then the topic has evolved on its own. High rate LTCs could be useful in practice: before attempting to decode a received word, one can save time by first quickly testing if it is close to the code. An outstanding open question has been whether there exist "c3-LTCs", namely LTCs with constant rate, constant distance, and constant locality. In this work we construct such codes based on a new two-dimensional complex which we call a left-right Cayley complex. This is essentially a graph which, in addition to vertices and edges, also has squares. Our codes can be viewed as a two-dimensional version of (the one-dimensional) expander codes, where the codewords are functions on the squares rather than on the edges.

Original languageAmerican English
Title of host publicationSTOC 2022 - Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing
EditorsStefano Leonardi, Anupam Gupta
PublisherAssociation for Computing Machinery
Pages357-374
Number of pages18
ISBN (Electronic)9781450392648
DOIs
StatePublished - 6 Sep 2022
Event54th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2022 - Rome, Italy
Duration: 20 Jun 202224 Jun 2022

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017

Conference

Conference54th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2022
Country/TerritoryItaly
CityRome
Period20/06/2224/06/22

Bibliographical note

Publisher Copyright:
© 2022 Owner/Author.

Keywords

  • error correcting codes
  • expander codes
  • locally testable codes

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