## Abstract

Interactive error correcting codesInteractive error correcting codes are codes that encode a two party communication protocol to an error-resilient protocol that succeeds even if a constant fraction of the communicated symbols are adversarially corrupted, at the cost of increasing the communication by a constant factor. What is the largest fraction of corruptions that such codes can protect against? If the error-resilient protocol is allowed to communicate large (constant sized) symbols, Braverman and Rao (STOC, 2011) show that the maximum rate of corruptions that can be tolerated is ¼. They also give a binary interactive error correcting protocol that only communicates bits and is resilient to ½ fraction of errors, but leave the optimality of this scheme as an open problem. We answer this question in the negative, breaking the 1/8 barrier. Specifically, we give a binary interactive error correcting scheme that is resilient to 5/39 > 1/8 fraction of adversarial errors. Our scheme builds upon a novel construction of binary list-decodable interactive codes with small list size.

Original language | English |
---|---|

Title of host publication | Proceedings - 2020 IEEE 61st Annual Symposium on Foundations of Computer Science, FOCS 2020 |

Publisher | Institute of Electrical and Electronics Engineers |

Pages | 470-481 |

Number of pages | 12 |

ISBN (Electronic) | 9781728196213 |

ISBN (Print) | 978-1-7281-9622-0 |

DOIs | |

State | Published - 19 Nov 2020 |

Event | 61st IEEE Annual Symposium on Foundations of Computer Science, FOCS 2020 - Virtual, Durham, United States Duration: 16 Nov 2020 → 19 Nov 2020 |

### Publication series

Name | Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS |
---|---|

Volume | 2020-November |

ISSN (Print) | 0272-5428 |

### Conference

Conference | 61st IEEE Annual Symposium on Foundations of Computer Science, FOCS 2020 |
---|---|

Country/Territory | United States |

City | Virtual, Durham |

Period | 16/11/20 → 19/11/20 |

## Keywords

- Communication Complexity
- Error Resilience
- Interactive Coding

## ASJC Scopus subject areas

- General Computer Science

## Fingerprint

Dive into the research topics of 'Binary Interactive Error Resilience Beyond 1/8 (or why (½)^{3}>1/8)'. Together they form a unique fingerprint.