Ldpc codes achieve list decoding capacity

Jonathan Mosheiff, Nicolas Resch, Noga Ron-Zewi, Shashwat Silas, Mary Wootters

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

15 Scopus citations

Abstract

We show that Gallager's ensemble of Low-Density Parity Check (LDPC) codes achieves list-decoding capacity with high probability. These are the first graph-based codes shown to have this property. This result opens up a potential avenue towards truly linear-time list-decodable codes that achieve list-decoding capacity. Our result on list decoding follows from a much more general result: Any local property satisfied with high probability by a random linear code is also satisfied with high probability by a random LDPC code from Gallager's distribution. Local properties are properties characterized by the exclusion of small sets of codewords, and include list-decoding, list-recovery and average-radius list-decoding. In order to prove our results on LDPC codes, we establish sharp thresholds for when local properties are satisfied by a random linear code. More precisely, we show that for any local property mathcal{P}, there is some R{ast} so that random linear codes of rate slightly less than R{ast} satisfy mathcal{P} with high probability, while random linear codes of rate slightly more than R{ast} with high probability do not. We also give a characterization of the threshold rate R{ast}. This is an extended abstract. The full version is available at https://arxiv.org/abs/1909.06430

Original languageEnglish
Title of host publicationProceedings - 2020 IEEE 61st Annual Symposium on Foundations of Computer Science, FOCS 2020
PublisherInstitute of Electrical and Electronics Engineers
Pages458-469
Number of pages12
ISBN (Electronic)9781728196213
DOIs
StatePublished - 1 Nov 2020
Externally publishedYes
Event61st IEEE Annual Symposium on Foundations of Computer Science, FOCS 2020 - Virtual, Durham, United States
Duration: 16 Nov 202019 Nov 2020

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
Volume2020-November
ISSN (Print)0272-5428

Conference

Conference61st IEEE Annual Symposium on Foundations of Computer Science, FOCS 2020
Country/TerritoryUnited States
CityVirtual, Durham
Period16/11/2019/11/20

Keywords

  • LDPC, List Decoding, Local Property, Thershold

ASJC Scopus subject areas

  • General Computer Science

Fingerprint

Dive into the research topics of 'Ldpc codes achieve list decoding capacity'. Together they form a unique fingerprint.

Cite this