Local list recovery of high-rate tensor codes and applications

Brett Hemenway, Noga Ron-Zewi, Mary Wootters

Research output: Contribution to journalArticlepeer-review

Abstract

We show that the tensor product of a high-rate globally list recoverable code is (approximately) locally list recoverable. List recovery has been a useful building block in the design of list decodable codes, and our motivation is to use the tensor construction as such a building block. In particular, instantiating this construction with known constructions of high-rate globally list recoverable codes, and using appropriate transformations, we obtain the first capacity-achieving locally list decodable codes (over a large constant size alphabet), and the first capacity-achieving globally list decodable codes with nearly linear time list decoding algorithms. Our techniques are inspired by an approach of Gopalan, Guruswami, and Raghavendra [SIAM J. Comput., 40 (2011), pp. 1432-1462] for list decoding tensor codes.

Original languageEnglish
Pages (from-to)157-195
Number of pages39
JournalSIAM Journal on Computing
Volume49
Issue number4
DOIs
StatePublished - 2020

Bibliographical note

Publisher Copyright:
© 2020 Society for Industrial and Applied Mathematics Publications. All rights reserved.

Keywords

  • List decoding
  • List recvoery
  • Local decoding

ASJC Scopus subject areas

  • General Computer Science
  • General Mathematics

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