Palette-alternating tree codes

Gil Cohen, Shahar Samocha

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

3 Scopus citations

Abstract

A tree code is an edge-coloring of the complete infinite binary tree such that every two nodes of equal depth have a fraction-bounded away from 0-of mismatched colors between the corresponding paths to their least common ancestor. Tree codes were introduced in a seminal work by Schulman [29] and serve as a key ingredient in almost all deterministic interactive coding schemes. The number of colors effects the coding scheme's rate. It is shown that 4 is precisely the least number of colors for which tree codes exist. Thus, tree-code-based coding schemes cannot achieve rate larger than 1/2. To overcome this barrier, a relaxed notion called palette-alternating tree codes is introduced, in which the number of colors can depend on the layer. We prove the existence of such constructs in which most layers use 2 colors-the bare minimum. The distance-rate tradeoff we obtain matches the Gilbert-Varshamov bound. Based on palette-alternating tree codes, we devise a deterministic interactive coding scheme against adversarial errors that approaches capacity. To analyze our protocol, we prove a structural result on the location of failed communication-rounds induced by the error pattern enforced by the adversary. Our coding scheme is efficient given an explicit palette-alternating tree code and serves as an alternative to the scheme obtained by [13].

Original languageEnglish
Title of host publication35th Computational Complexity Conference, CCC 2020
EditorsShubhangi Saraf
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771566
DOIs
StatePublished - 1 Jul 2020
Event35th Computational Complexity Conference, CCC 2020 - Virtual, Online, Germany
Duration: 28 Jul 202031 Jul 2020

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume169
ISSN (Print)1868-8969

Conference

Conference35th Computational Complexity Conference, CCC 2020
Country/TerritoryGermany
CityVirtual, Online
Period28/07/2031/07/20

Funding

FundersFunder number
Israel Science Foundation1569/18

    Keywords

    • Coding Theory
    • Interactive Coding Scheme
    • Tree Codes

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