# Reliable communication over highly connected noisy networks

## Author(s): Alon, N; Braverman, Mark; Efremenko, K; Gelles, Ran; Haeupler, B

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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). |

Publication Date: | 25-Jul-2016 |

Electronic Publication Date: | 2016 |

Citation: | Alon, N, Braverman, M, Efremenko, K, Gelles, R, Haeupler, B. (2017). Reliable communication over highly connected noisy networks. Distributed Computing, 1 - 11. doi:10.1007/s00446-017-0303-5 |

DOI: | doi:10.1145/2933057.2933085 |

Pages: | 1 - 11 |

Type of Material: | Conference Article |

Journal/Proceeding Title: | PODC '16 Proceedings of the 2016 ACM Symposium on Principles of Distributed Computing |

Version: | Author's manuscript |

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