## 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 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/m^{3} 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 n^{ω(1)}.

Original language | English |
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Title of host publication | PODC 2016 - Proceedings of the 2016 ACM Symposium on Principles of Distributed Computing |

Publisher | Association for Computing Machinery |

Pages | 165-173 |

Number of pages | 9 |

ISBN (Electronic) | 9781450339643 |

DOIs | |

State | Published - 25 Jul 2016 |

Externally published | Yes |

Event | 35th ACM Symposium on Principles of Distributed Computing, PODC 2016 - Chicago, United States Duration: 25 Jul 2016 → 28 Jul 2016 |

### Publication series

Name | Proceedings of the Annual ACM Symposium on Principles of Distributed Computing |
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Volume | 25-28-July-2016 |

### Conference

Conference | 35th ACM Symposium on Principles of Distributed Computing, PODC 2016 |
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Country/Territory | United States |

City | Chicago |

Period | 25/07/16 → 28/07/16 |

### Bibliographical note

Publisher Copyright:© 2016 ACM.

### Funding

Research supported in part by a USA-Israeli BSF grant, by an ISF grant, by the Israeli I-Core program and by the Oswald Veblen Fund. Research supported in part by an NSF CAREER award (CCF-1149888), a Turing Centenary Fellowship, a Packard Fellowship in Science and Engineering, and the Simons Collaboration on Algorithms and Geometry. Research supported in part by: European Communitys Seventh Framework Programme (FP7/2007-2013) under grant agreement number 257575.

Funders | Funder number |
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Israeli I-Core | |

Oswald Veblen Fund | |

USA-Israeli BSF | |

National Science Foundation | CCF-1149888 |

Seventh Framework Programme | 257575 |

Israel Science Foundation | |

Seventh Framework Programme |