Singleton-type bounds for list-decoding and list-recovery, and related results

Eitan Goldberg, Chong Shangguan, Itzhak Tamo

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

Abstract

We prove a new Singleton-type upper bound for list-decodable codes, which improves upon the previously known bound by roughly a factor of 1/L, where L is the list size. We also prove a Singleton-type upper bound for list-recoverable codes, which to the best of our knowledge, is the first such bound. Then, we apply these results to obtain new lower bounds on the list size of list-decodable or recoverable codes with rates approaching capacity, that are optimal up to a multiplicative constant.Moreover, we show that for a wide range of parameters, list-decodable nonlinear codes can strictly outperform list-decodable linear codes. This is achieved by a novel connection between list-decoding and the notion of sparse hypergraphs in extremal combinatorics. Lastly, we show that list-decodability or recover-ability of codes implies in some sense good unique decodability.The full version of the paper is accessible at [1].

Original languageEnglish
Title of host publication2022 IEEE International Symposium on Information Theory, ISIT 2022
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2565-2570
Number of pages6
ISBN (Electronic)9781665421591
DOIs
StatePublished - 2022
Event2022 IEEE International Symposium on Information Theory, ISIT 2022 - Espoo, Finland
Duration: 26 Jun 20221 Jul 2022

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2022-June
ISSN (Print)2157-8095

Conference

Conference2022 IEEE International Symposium on Information Theory, ISIT 2022
Country/TerritoryFinland
CityEspoo
Period26/06/221/07/22

Funding

FundersFunder number
European Research Council852953
National Natural Science Foundation of China12101364
Israel Science Foundation1030/15
Natural Science Foundation of Shandong ProvinceZR2021QA005
National Key Research and Development Program of China2021YFA1001000

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