Capacity of interactive communication over erasure channels and channels with feedback

Ran Gelles; Bernhard Haeupler

doi:10.1137/15m1052202

Capacity of interactive communication over erasure channels and channels with feedback

Ran Gelles, Bernhard Haeupler

Bar-Ilan University - The Alexander Kofkin Faculty of Engineering

Carnegie Mellon University

Research output: Contribution to journal › Article › peer-review

18 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 language	English
Pages (from-to)	1449-1472
Number of pages	24
Journal	SIAM Journal on Computing
Volume	46
Issue number	4
DOIs	https://doi.org/10.1137/15m1052202
State	Published - 2017

Bibliographical note

Publisher Copyright:
© 2017 SIAM.

Funding

∗Received by the editors December 10, 2015; accepted for publication (in revised form) May 19, 2017; published electronically August 17, 2017. A preliminary version of this paper appeared in SODA’15, SIAM, Philadelphia, 2015, pp. 1296–1311. http://www.siam.org/journals/sicomp/46-4/M105220.html Funding: The second author was supported in part by NSF grants CCF-1527110 and CCF-1618280. †Faculty of Engineering, Bar-Ilan University, Ramat-gan, 5290002, Israel ([email protected]). Part of this work was done while at UCLA and Princeton University. ‡Computer Science Department, Carnegie Mellon University, Pittsburgh, PA 15213 (haeupler@ cs.cmu.edu).

Funders	Funder number
National Science Foundation	CCF-1618280, 1527110, CCF-1527110

Keywords

Channels with feedback
Erasure channels
Interactive channel capacity
Interactive coding

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10.1137/15m1052202

Cite this

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Capacity of interactive communication over erasure channels and channels with feedback

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