Interactive coding over the noisy broadcast channel

Klim Efremenko, Gillat Kol, Raghuvansh Saxena

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

A set of n players, each holding a private input bit, communicate over a noisy broadcast channel. Their mutual goal is for all players to learn all inputs. At each round one of the players broadcasts a bit to all the other players, and the bit received by each player is flipped with a fixed constant probability (independently for each recipient). How many rounds are needed? This problem was first suggested by El Gamal in 1984. In 1988, Gallager gave an elegant noise-resistant protocol requiring only O(n log log n) rounds. The problem got resolved in 2005 by a seminal paper of Goyal, Kindler, and Saks, proving that Gallager’s protocol is essentially optimal. We revisit the above noisy broadcast problem and show that O(n) rounds suffice. This is possible due to a relaxation of the model assumed by the previous works. We no longer demand that exactly one player broadcasts in every round, but rather allow any number of players to broadcast. However, if it is not the case that exactly one player chooses to broadcast, each of the other players gets an adversely chosen bit. We generalized the above result and initiate the study of interactive coding over the noisy broadcast channel. We show that any interactive protocol that works over the noiseless broadcast channel can be simulated over our restrictive noisy broadcast model with constant blowup of the communication.

Original languageEnglish (US)
Title of host publicationSTOC 2018 - Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing
EditorsMonika Henzinger, David Kempe, Ilias Diakonikolas
PublisherAssociation for Computing Machinery
Pages890-901
Number of pages12
ISBN (Electronic)9781450355599
DOIs
StatePublished - Jun 20 2018
Event50th Annual ACM Symposium on Theory of Computing, STOC 2018 - Los Angeles, United States
Duration: Jun 25 2018Jun 29 2018

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017

Other

Other50th Annual ACM Symposium on Theory of Computing, STOC 2018
CountryUnited States
CityLos Angeles
Period6/25/186/29/18

All Science Journal Classification (ASJC) codes

  • Software

Keywords

  • Communication complexity
  • Interactive coding
  • Wireless broadcast

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