Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH scholarly article en Haeupler, Bernhard; Kamath, Pritish; Velingker, Ameya http://www.dagstuhl.de/lipics License
when quoting this document, please refer to the following
DOI:
URN: urn:nbn:de:0030-drops-53426
URL:

; ;

Communication with Partial Noiseless Feedback

pdf-format:


Abstract

We introduce the notion of one-way communication schemes with partial noiseless feedback. In this setting, Alice wishes to communicate a message to Bob by using a communication scheme that involves sending a sequence of bits over a channel while receiving feedback bits from Bob for delta fraction of the transmissions. An adversary is allowed to corrupt up to a constant fraction of Alice's transmissions, while the feedback is always uncorrupted. Motivated by questions related to coding for interactive communication, we seek to determine the maximum error rate, as a function of 0 <= delta <= 1, such that Alice can send a message to Bob via some protocol with delta fraction of noiseless feedback. The case delta = 1 corresponds to full feedback, in which the result of Berlekamp ['64] implies that the maximum tolerable error rate is 1/3, while the case delta = 0 corresponds to no feedback, in which the maximum tolerable error rate is 1/4, achievable by use of a binary error-correcting code. In this work, we show that for any delta in (0,1] and gamma in [0, 1/3), there exists a randomized communication scheme with noiseless delta-feedback, such that the probability of miscommunication is low, as long as no more than a gamma fraction of the rounds are corrupted. Moreover, we show that for any delta in (0, 1] and gamma < f(delta), there exists a deterministic communication scheme with noiseless delta-feedback that always decodes correctly as long as no more than a gamma fraction of rounds are corrupted. Here f is a monotonically increasing, piecewise linear, continuous function with f(0) = 1/4 and f(1) = 1/3. Also, the rate of communication in both cases is constant (dependent on delta and gamma but independent of the input length).

BibTeX - Entry

@InProceedings{haeupler_et_al:LIPIcs:2015:5342,
  author =	{Bernhard Haeupler and Pritish Kamath and Ameya Velingker},
  title =	{{Communication with Partial Noiseless Feedback}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)},
  pages =	{881--897},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-89-7},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{40},
  editor =	{Naveen Garg and Klaus Jansen and Anup Rao and Jos{\'e} D. P. Rolim},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/5342},
  URN =		{urn:nbn:de:0030-drops-53426},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2015.881},
  annote =	{Keywords: Communication with feedback, Interactive communication, Coding theory Digital}
}

Keywords: Communication with feedback, Interactive communication, Coding theory Digital
Seminar: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)
Issue date: 2015
Date of publication: 2015


DROPS-Home | Fulltext Search | Imprint Published by LZI