## Abstract

In the field of interactive coding, two or more parties wish to carry out a distributed computation over a communication network that may be noisy. The ultimate goal is to develop efficient coding schemes that can tolerate a high level of noise while increasing the communication by only a constant factor (i.e., constant rate). In this work we consider synchronous communication networks over an arbitrary topology, in the powerful adversarial insertion-deletion noise model. Namely, the noisy channel may adversarially alter the content of any transmitted symbol, as well as completely remove a transmitted symbol or inject a new symbol into the channel. We provide efficient, constant rate schemes that successfully conduct any computation with high probability as long as the adversary corrupts at most over m fraction of the total communication, where m is the number of links in the network and is a small constant. This scheme assumes an oblivious adversary which is independent of the parties' inputs and randomness. We can remove this assumption and resist a worst-case adversary at the price of being resilient to over m log m errors. While previous work considered the insertion-deletion noise model in the two-party setting, to the best of our knowledge, our scheme is the first multiparty scheme that is resilient to insertions and deletions. Furthermore, our scheme is the first computationally efficient scheme in the multiparty setting that is resilient to adversarial noise.

Original language | English |
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Title of host publication | PODC 2019 - Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing |

Publisher | Association for Computing Machinery |

Pages | 137-146 |

Number of pages | 10 |

ISBN (Electronic) | 9781450362177 |

DOIs | |

State | Published - 16 Jul 2019 |

Event | 38th ACM Symposium on Principles of Distributed Computing, PODC 2019 - Toronto, Canada Duration: 29 Jul 2019 → 2 Aug 2019 |

### Publication series

Name | Proceedings of the Annual ACM Symposium on Principles of Distributed Computing |
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### Conference

Conference | 38th ACM Symposium on Principles of Distributed Computing, PODC 2019 |
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Country/Territory | Canada |

City | Toronto |

Period | 29/07/19 → 2/08/19 |

### Bibliographical note

Publisher Copyright:© 2019 ACM.

### Funding

Supported in part by the Israel Science Foundation (ISF) through grant No. 1078/17. Supported in part by NSF award CCF 1665252 and NSF award DMS-1737944.

Funders | Funder number |
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National Science Foundation | DMS-1737944, CCF 1665252 |

Directorate for Mathematical and Physical Sciences | 1737944 |

Israel Science Foundation | 1078/17 |

## Keywords

- Distributed algorithms
- Error correcting codes
- Interactive coding