License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2021.25
URN: urn:nbn:de:0030-drops-140942
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14094/
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Ben Basat, Ran ; Mitzenmacher, Michael ; Vargaftik, Shay

How to Send a Real Number Using a Single Bit (And Some Shared Randomness)

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LIPIcs-ICALP-2021-25.pdf (0.9 MB)

Abstract

We consider the fundamental problem of communicating an estimate of a real number x ∈ [0,1] using a single bit. A sender that knows x chooses a value X ∈ {0,1} to transmit. In turn, a receiver estimates x based on the value of X. The goal is to minimize the cost, defined as the worst-case (over the choice of x) expected squared error.
We first overview common biased and unbiased estimation approaches and prove their optimality when no shared randomness is allowed. We then show how a small amount of shared randomness, which can be as low as a single bit, reduces the cost in both cases. Specifically, we derive lower bounds on the cost attainable by any algorithm with unrestricted use of shared randomness and propose optimal and near-optimal solutions that use a small number of shared random bits. Finally, we discuss open problems and future directions.

BibTeX - Entry

@InProceedings{benbasat_et_al:LIPIcs.ICALP.2021.25,
  author =	{Ben Basat, Ran and Mitzenmacher, Michael and Vargaftik, Shay},
  title =	{{How to Send a Real Number Using a Single Bit (And Some Shared Randomness)}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{25:1--25:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14094},
  URN =		{urn:nbn:de:0030-drops-140942},
  doi =		{10.4230/LIPIcs.ICALP.2021.25},
  annote =	{Keywords: Randomized Algorithms, Approximation Algorithms, Shared Randomness, Distributed Protocols, Estimation, Subtractive Dithering}
}

Keywords: Randomized Algorithms, Approximation Algorithms, Shared Randomness, Distributed Protocols, Estimation, Subtractive Dithering
Collection: 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)
Issue Date: 2021
Date of publication: 02.07.2021

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