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Distributed Computing

, Volume 32, Issue 6, pp 505–515 | Cite as

Reliable communication over highly connected noisy networks

  • Noga Alon
  • Mark Braverman
  • Klim Efremenko
  • Ran GellesEmail author
  • Bernhard Haeupler
Article
  • 90 Downloads

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 \(\liminf _{n,R\rightarrow \infty } R/R'\) 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 \(O(1/m^3\log m)\). 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 \(n^{\varOmega (1)}\).

Keywords

Coding theory Random noise Interactive coding Computation with noise 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Sackler School of Mathematics and Blavatnik School of Computer ScienceTel Aviv UniversityTel AvivIsrael
  2. 2.Department of Computer SciencePrinceton UniversityPrincetonUSA
  3. 3.Department of Computer ScienceTel Aviv UniversityTel AvivIsrael
  4. 4.Faculty of EngineeringBar-Ilan UniversityRamat GanIsrael
  5. 5.Department of Computer ScienceCarnegie Mellon UniversityPittsburghUSA

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