Tight Bounds for General Computation in Noisy Broadcast Networks

Klim Efremenko, Gillat Kol, Dmitry Paramonov, Raghuvansh R. Saxena

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Let II be a protocol over the n-party broadcast channel, where in each round, a pre-specified party broadcasts a symbol to all other parties. We wish to design a scheme that takes such a protocol II as input and outputs a noise resilient protocol II' that simulates II over the noisy broadcast channel, where each received symbol is flipped with a fixed constant probability, independently. What is the minimum overhead in the number of rounds that is incurred by any such simulation scheme? A classical result by Gallager from the 80's shows that non-interactive T-round protocols, where the bit communicated in every round is independent of the communication history, can be converted to noise resilient ones with only an O}(log log T) multiplicative overhead in the number of rounds. Can the same be proved for any protocol? Or, are there protocols whose simulation requires an Ω(log T) overhead (which always suffices)? We answer both the above questions in the negative: We give a simulation scheme with an tildeO(√{ log T}) overhead for every protocol and channel alphabet. We also prove an (almost) matching lower bound of Ω(√{ log T}) on the overhead required to simulate the pointer chasing protocol with T = n and polynomial alphabet.

Original languageEnglish
Title of host publicationProceedings - 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science, FOCS 2021
PublisherIEEE Computer Society
Pages634-645
Number of pages12
ISBN (Electronic)9781665420556
DOIs
StatePublished - 2021
Event62nd IEEE Annual Symposium on Foundations of Computer Science, FOCS 2021 - Virtual, Online, United States
Duration: 7 Feb 202210 Feb 2022

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
Volume2022-February
ISSN (Print)0272-5428

Conference

Conference62nd IEEE Annual Symposium on Foundations of Computer Science, FOCS 2021
Country/TerritoryUnited States
CityVirtual, Online
Period7/02/2210/02/22

ASJC Scopus subject areas

  • Computer Science (all)

Fingerprint

Dive into the research topics of 'Tight Bounds for General Computation in Noisy Broadcast Networks'. Together they form a unique fingerprint.

Cite this