LCC and LDC: Tailor-Made Distance Amplification and a Refined Separation

Gil Cohen, Tal Yankovitz

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

Abstract

The Alon-Edmonds-Luby distance amplification procedure (FOCS 1995) is an algorithm that transforms a code with vanishing distance to a code with constant distance. AEL was invoked by Kopparty, Meir, Ron-Zewi, and Saraf (J. ACM 2017) for obtaining their state-of-the-art LDC, LCC and LTC. Cohen and Yankovitz (CCC 2021) devised a procedure that can amplify inverse-polynomial distances, exponentially extending the regime of distances that can be amplified by AEL. However, the improved procedure only works for LDC and assuming rate (Equation presented). 1 In this work we devise a distance amplification procedure for LCC with inverse-polynomial distances even for vanishing rate (Equation presented). For LDC, we obtain a more modest improvement and require rate (Equation presented). Thus, the tables have turned and it is now LCC that can be better amplified. Our key idea for accomplishing this, deviating from prior work, is to tailor the distance amplification procedure to the code at hand. Our second result concerns the relation between linear LDC and LCC. We prove the existence of linear LDC that are not LCC, qualitatively extending a separation by Kaufman and Viderman (RANDOM 2010).

Original languageEnglish
Title of host publication49th EATCS International Conference on Automata, Languages, and Programming, ICALP 2022
EditorsMikolaj Bojanczyk, Emanuela Merelli, David P. Woodruff
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959772358
DOIs
StatePublished - 1 Jul 2022
Event49th EATCS International Conference on Automata, Languages, and Programming, ICALP 2022 - Paris, France
Duration: 4 Jul 20228 Jul 2022

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume229
ISSN (Print)1868-8969

Conference

Conference49th EATCS International Conference on Automata, Languages, and Programming, ICALP 2022
Country/TerritoryFrance
CityParis
Period4/07/228/07/22

Keywords

  • Distance Amplifications
  • Locally Correctable Codes
  • Locally Decodable Codes

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