Linear-time Erasure List-decoding of Expander Codes

Noga Ron-Zewi, Mary Wootters, Gilles Zemor

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


We give a linear-time erasure list-decoding algorithm for expander codes. More precisely, let r > 0 be any integer. Given an inner code C0 of length d, and a d-regular bipartite expander graph G with n vertices on each side, we give an algorithm to list-decode the expander code C = C GC0} of length nd from approximately δδrnd erasures in time n·poly(d2r/δ), where δ and δr are the relative distance and the r'th·generalized relative distance of C0, respectively. To the best of our knowledge, this is the first linear-time algorithm that can list-decode expander codes from erasures beyond their (designed) distance of approximately δ2nd.To obtain our results, we show that an approach similar to that of (Hemenway and Wootters, Information and Computation, 2018) can be used to obtain such an erasure-list-decoding algorithm with an exponentially worse dependence of the running time on r and δ; then we show how to improve the dependence of the running time on these parameters.

Original languageEnglish
Title of host publication2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages5
ISBN (Electronic)9781728164328
StatePublished - Jun 2020
Event2020 IEEE International Symposium on Information Theory, ISIT 2020 - Los Angeles, United States
Duration: 21 Jul 202026 Jul 2020

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8095


Conference2020 IEEE International Symposium on Information Theory, ISIT 2020
Country/TerritoryUnited States
CityLos Angeles

Bibliographical note

Publisher Copyright:
© 2020 IEEE.

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics


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