Local list recovery of high-rate tensor codes & applications

Brett Hemenway, Noga Ron-Zewi, Mary Wootters

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

17 Scopus citations

Abstract

In this work, we give the first construction of high-rate locally list-recoverable codes. List-recovery has been an extremely useful building block in coding theory, and our motivation is to use these codes as such a building block. In particular, our construction gives the first capacity-achieving locally list-decodable codes (over constant-sized alphabet); the first capacity achieving} globally list-decodable codes with nearly linear time list decoding algorithm (once more, over constant-sized alphabet); and a randomized construction of binary codes on the Gilbert-Varshamov bound that can be uniquely decoded in near-linear-time, with higher rate than was previously known.Our techniques are actually quite simple, and are inspired by an approach of Gopalan, Guruswami, and Raghavendra (Siam Journal on Computing, 2011) for list-decoding tensor codes. We show that tensor powers of (globally) list-recoverable codes are approximately locally list-recoverable, and that the approximately modifier may be removed by pre-encoding the message with a suitable locally decodable code. Instantiating this with known constructions of high-rate globally list-recoverable codes and high-rate locally decodable codes finishes the construction.

Original languageEnglish
Title of host publicationProceedings - 58th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2017
PublisherIEEE Computer Society
Pages204-215
Number of pages12
ISBN (Electronic)9781538634646
DOIs
StatePublished - 10 Nov 2017
Event58th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2017 - Berkeley, United States
Duration: 15 Oct 201717 Oct 2017

Publication series

NameAnnual Symposium on Foundations of Computer Science - Proceedings
Volume2017-October
ISSN (Print)0272-5428

Conference

Conference58th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2017
Country/TerritoryUnited States
CityBerkeley
Period15/10/1717/10/17

Keywords

  • coding theory
  • error correcting codes
  • list recovery
  • local list recovery
  • tensor codes

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