TY - GEN

T1 - Palette-alternating tree codes

AU - Cohen, Gil

AU - Samocha, Shahar

N1 - Publisher Copyright:
© Gil Cohen and Shahar Samocha; licensed under Creative Commons License CC-BY 35th Computational Complexity Conference (CCC 2020).

PY - 2020/7/1

Y1 - 2020/7/1

N2 - 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].

AB - 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].

KW - Coding Theory

KW - Interactive Coding Scheme

KW - Tree Codes

UR - http://www.scopus.com/inward/record.url?scp=85089374430&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.CCC.2020.11

DO - 10.4230/LIPIcs.CCC.2020.11

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:85089374430

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 35th Computational Complexity Conference, CCC 2020

A2 - Saraf, Shubhangi

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 35th Computational Complexity Conference, CCC 2020

Y2 - 28 July 2020 through 31 July 2020

ER -