Interactive error resilience beyond 2/7

Klim Efremenko, Gillat Kol, Raghuvansh R. Saxena

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Interactive error correcting codes can protect interactive communication protocols against a constant fraction of adversarial errors, while incurring only a constant multiplicative overhead in the total communication. What is the maximum fraction of errors that such codes can protect against? For the non-adaptive channel, where the parties must agree in advance on the order in which they communicate, Braverman and Rao prove that the maximum error resilience is 1/4 (STOC, 2011). Ghaffari, Haeupler, and Sudan (STOC, 2014) consider the adaptive channel, where the order in which the parties communicate may not be fixed, and give a clever protocol that is resilient to a 2/7 fraction of errors. This was believed to be optimal. We revisit this result, and show how to overcome the 2/7 barrier. Specifically, we show that, over the adaptive channel, every two-party communication protocol can be converted to a protocol that is resilient to 7/24 > 2/7 fraction of errors with only a constant multiplicative overhead to the total communication. The protocol is obtained by a novel implementation of a feedback mechanism over the adaptive channel.

Original languageEnglish (US)
Title of host publicationSTOC 2020 - Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing
EditorsKonstantin Makarychev, Yury Makarychev, Madhur Tulsiani, Gautam Kamath, Julia Chuzhoy
PublisherAssociation for Computing Machinery
Pages565-578
Number of pages14
ISBN (Electronic)9781450369794
DOIs
StatePublished - Jun 8 2020
Event52nd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2020 - Chicago, United States
Duration: Jun 22 2020Jun 26 2020

Publication series

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

Conference

Conference52nd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2020
CountryUnited States
CityChicago
Period6/22/206/26/20

All Science Journal Classification (ASJC) codes

  • Software

Keywords

  • Communication Complexity
  • Error Resilience
  • Interactive Coding

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  • Cite this

    Efremenko, K., Kol, G., & Saxena, R. R. (2020). Interactive error resilience beyond 2/7. In K. Makarychev, Y. Makarychev, M. Tulsiani, G. Kamath, & J. Chuzhoy (Eds.), STOC 2020 - Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing (pp. 565-578). (Proceedings of the Annual ACM Symposium on Theory of Computing). Association for Computing Machinery. https://doi.org/10.1145/3357713.3384320