Reliable Communication over Highly Connected Noisy Networks

Noga Alon, Mark Braverman, Klim Efremenko, Ran Gelles, Bernhard Haeupler

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

21 Scopus citations

Abstract

We consider the task of multiparty computation performed over networks in the presence of random noise. Given an n-party protocol that takes R rounds assuming noiseless communication, the goal is to find a coding scheme that takes R′ rounds and computes the same function with high probability even when the communication is noisy, while maintaining a constant asymptotic rate, i.e., while keeping lim infn,R→∞ R/R′ positive. Rajagopalan and Schulman (STOC '94) were the first to consider this question, and provided a coding scheme with rate O(1= log(d + 1)), where d is the maximal degree in the network. While that scheme provides a constant rate coding for many practical situations, in the worst case, e.g., when the network is a complete graph, the rate is O(1= log n), which tends to 0 as n tends to infinity. We revisit this question and provide an efficient coding scheme with a constant rate for the interesting case of fully connected networks. We furthermore extend the result and show that if a (d-regular) network has mixing time m, then there exists an efficient coding scheme with rate O(1/m3 logm). This implies a constant rate coding scheme for any n-party protocol over a d-regular network with a constant mixing time, and in particular for random graphs with n vertices and degrees nω(1).

Original languageEnglish
Title of host publicationPODC 2016 - Proceedings of the 2016 ACM Symposium on Principles of Distributed Computing
Place of PublicationNew York
PublisherAssociation for Computing Machinery
Pages165–173
Number of pages9
ISBN (Electronic)9781450339643
DOIs
StatePublished - 25 Jul 2016
Externally publishedYes
Event35th ACM Symposium on Principles of Distributed Computing, PODC 2016 - Chicago, United States
Duration: 25 Jul 201628 Jul 2016

Conference

Conference35th ACM Symposium on Principles of Distributed Computing, PODC 2016
Country/TerritoryUnited States
CityChicago
Period25/07/1628/07/16

Keywords

  • communication complexity
  • coding theorey
  • interactive coding
  • random noise
  • multiparty protocols

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