Explicit binary tree codes with sub-logarithmic size alphabet

Inbar Ben Yaacov, Gil Cohen, Tal Yankovitz

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

Abstract

Since they were first introduced by Schulman (STOC 1993), the construction of tree codes remained an elusive open problem. The state-of-the-art construction by Cohen, Haeupler and Schulman (STOC 2018) has constant distance and (logn)e colors for some constant e > 1 that depends on the distance, where n is the depth of the tree. Insisting on a constant number of colors at the expense of having vanishing distance, Gelles, Haeupler, Kol, Ron-Zewi, and Wigderson (SODA 2016) constructed a distance ω(1/logn) tree code. In this work we improve upon these prior works and construct a distance-δtree code with (logn)O(s) colors. This is the first construction of a constant distance tree code with sub-logarithmic number of colors. Moreover, as a direct corollary we obtain a tree code with a constant number of colors and distance ω(1/(loglogn)2), exponentially improving upon the above-mentioned work by Gelles et al.

Original languageEnglish
Title of host publicationSTOC 2022 - Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing
EditorsStefano Leonardi, Anupam Gupta
PublisherAssociation for Computing Machinery
Pages595-608
Number of pages14
ISBN (Electronic)9781450392648
DOIs
StatePublished - 6 Sep 2022
Externally publishedYes
Event54th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2022 - Rome, Italy
Duration: 20 Jun 202224 Jun 2022

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017

Conference

Conference54th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2022
Country/TerritoryItaly
CityRome
Period20/06/2224/06/22

Keywords

  • explicit constructions
  • tree codes

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