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Optimal error resilience of adaptive message exchange

Published: 15 June 2021 Publication History

Abstract

We study the error resilience of the message exchange task: Two parties, each holding a private input, want to exchange their inputs. However, the channel connecting them is governed by an adversary that may corrupt a constant fraction of the transmissions. What is the maximum fraction of corruptions that still allows the parties to exchange their inputs?
For the non-adaptive channel, where the parties must agree in advance on the order in which they communicate, the maximum error resilience was shown to be 1/4 (see Braverman and Rao, STOC 2011). The problem was also studied over the adaptive channel, where the order in which the parties communicate may not be predetermined (Ghaffari, Haeupler, and Sudan, STOC 2014; Efremenko, Kol, and Saxena, STOC 2020). These works show that the adaptive channel admits much richer set of protocols but leave open the question of finding its maximum error resilience.
In this work, we show that the maximum error resilience of a protocol for message exchange over the adaptive channel is 5/16, thereby settling the above question. Our result requires improving both the known upper bounds and the known lower bounds for the problem.

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  • (2022)Binary Codes with Resilience Beyond 1/4 via Interaction2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS54457.2022.00008(1-12)Online publication date: Oct-2022
  • (2022)Tight Bounds for General Computation in Noisy Broadcast Networks2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS52979.2021.00068(634-645)Online publication date: Feb-2022

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    cover image ACM Conferences
    STOC 2021: Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing
    June 2021
    1797 pages
    ISBN:9781450380539
    DOI:10.1145/3406325
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    Published: 15 June 2021

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    Author Tags

    1. Communication Complexity
    2. Error Resilience
    3. Interactive Coding

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    • (2022)Binary Codes with Resilience Beyond 1/4 via Interaction2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS54457.2022.00008(1-12)Online publication date: Oct-2022
    • (2022)Tight Bounds for General Computation in Noisy Broadcast Networks2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS52979.2021.00068(634-645)Online publication date: Feb-2022

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