@inproceedings{75a99ce0d27b41f39f4a7584b711c760,
title = "Explicit binary tree codes with sub-logarithmic size alphabet",
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.",
keywords = "explicit constructions, tree codes",
author = "{Ben Yaacov}, Inbar and Gil Cohen and Tal Yankovitz",
note = "Publisher Copyright: {\textcopyright} 2022 ACM.; 54th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2022 ; Conference date: 20-06-2022 Through 24-06-2022",
year = "2022",
month = sep,
day = "6",
doi = "https://doi.org/10.1145/3519935.3520033",
language = "الإنجليزيّة",
series = "Proceedings of the Annual ACM Symposium on Theory of Computing",
publisher = "Association for Computing Machinery",
pages = "595--608",
editor = "Stefano Leonardi and Anupam Gupta",
booktitle = "STOC 2022 - Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing",
address = "الولايات المتّحدة",
}