TY - JOUR

T1 - Reliable communication over highly connected noisy networks

AU - Alon, Noga

AU - Braverman, Mark

AU - Efremenko, Klim

AU - Gelles, Ran

AU - Haeupler, Bernhard

N1 - Publisher Copyright:
© 2017, Springer-Verlag Berlin Heidelberg.

PY - 2019/12/1

Y1 - 2019/12/1

N2 - 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 inf n , 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 / m3log 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 nΩ ( 1 ).

AB - 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 inf n , 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 / m3log 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 nΩ ( 1 ).

KW - Coding theory

KW - Computation with noise

KW - Interactive coding

KW - Random noise

UR - http://www.scopus.com/inward/record.url?scp=85019674698&partnerID=8YFLogxK

U2 - 10.1007/s00446-017-0303-5

DO - 10.1007/s00446-017-0303-5

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AN - SCOPUS:85019674698

SN - 0178-2770

VL - 32

SP - 505

EP - 515

JO - Distributed Computing

JF - Distributed Computing

IS - 6

ER -