TY - GEN

T1 - Explicit binary tree codes with sub-logarithmic size alphabet

AU - Ben Yaacov, Inbar

AU - Cohen, Gil

AU - Yankovitz, Tal

N1 - Publisher Copyright:
© 2022 ACM.

PY - 2022/9/6

Y1 - 2022/9/6

N2 - 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.

AB - 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.

KW - explicit constructions

KW - tree codes

UR - http://www.scopus.com/inward/record.url?scp=85132779191&partnerID=8YFLogxK

U2 - 10.1145/3519935.3520033

DO - 10.1145/3519935.3520033

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AN - SCOPUS:85132779191

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 595

EP - 608

BT - STOC 2022 - Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing

A2 - Leonardi, Stefano

A2 - Gupta, Anupam

PB - Association for Computing Machinery

T2 - 54th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2022

Y2 - 20 June 2022 through 24 June 2022

ER -