Capacity of interactive communication over erasure channels and channels with feedback

Ran Gelles, Bernhard Haeupler

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

We consider interactive communication performed over two types of noisy channels: binary error channels with noiseless feedback and binary erasure channels. In both cases, the noise model is adversarial. Assuming at most ϵ-fraction of the bits can be corrupted, we show coding schemes that simulate any alternating interactive protocol with rate 1-Θ(H(ϵ)). All our simulations are simple, randomized, and computationally efficient. The rates of our coding schemes stand in contrast to the interactive communication rates supported by random or adversarial error channels without feedback, for which the best known coding schemes achieve rates of 1 - Θ(√ϵ) and 1 - Θ(√ϵ log log 1/ϵ), respectively. As these rates are conjectured to be optimal, our result implies a large asymptotic gap between interactive communication rates over noisy channels with and without feedback. Such a gap has no equivalent in the standard one-way communication setting.

Original languageEnglish
Pages (from-to)1449-1472
Number of pages24
JournalSIAM Journal on Computing
Volume46
Issue number4
DOIs
StatePublished - 2017

Bibliographical note

Publisher Copyright:
© 2017 SIAM.

Keywords

  • Channels with feedback
  • Erasure channels
  • Interactive channel capacity
  • Interactive coding

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