The Rate of Interactive Codes Is Bounded Away from 1

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

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


Kol and Raz [STOC 2013] showed how to simulate any alternating two-party communication protocol designed to work over the noiseless channel, by a protocol that works over a stochastic channel that corrupts each sent symbol with probability., ">0 independently, with only a 1+O((")) blowup to the communication. In particular, this implies that the maximum rate of such interactive codes approaches 1 as "goes to0, as is also the case for the maximum rate of classical error correcting codes. Over the past decade, followup works have strengthened and generalized this result to other noisy channels, stressing on how fast the rate approaches 1 as "goes to 0, but retaining the assumption that the noiseless protocol is alternating. In this paper we consider the general case, where the noiseless protocols can have arbitrary orders of speaking. In contrast to Kol-Raz and to the followup results in this model, we show that the maximum rate of interactive codes that encode general protocols is upper bounded by a universal constant strictly smaller than 1. To put it differently, we show that there is an inherent blowup in communication when protocols with arbitrary orders of speaking are faced with any constant fraction of errors., "> 0. We mention that our result assumes a large alphabet set and resolves the (non-binary variant) of a conjecture by Haeupler [FOCS2014].

Original languageEnglish
Title of host publicationSTOC 2023 - Proceedings of the 55th Annual ACM Symposium on Theory of Computing
EditorsBarna Saha, Rocco A. Servedio
PublisherAssociation for Computing Machinery
Number of pages14
ISBN (Electronic)9781450399135
StatePublished - 2 Jun 2023
Event55th Annual ACM Symposium on Theory of Computing, STOC 2023 - Orlando, United States
Duration: 20 Jun 202323 Jun 2023

Publication series

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


Conference55th Annual ACM Symposium on Theory of Computing, STOC 2023
Country/TerritoryUnited States


  • Communication Complexity
  • Error Correcting Codes
  • Interactive Coding

ASJC Scopus subject areas

  • Software


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