License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2015.867
URN: urn:nbn:de:0030-drops-53417
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2015/5341/
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Guruswami, Venkatesan ; Wang, Carol

Deletion Codes in the High-noise and High-rate Regimes

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Abstract

The noise model of deletions poses significant challenges in coding theory, with basic questions like the capacity of the binary deletion channel still being open. In this paper, we study the harder model of worst-case deletions, with a focus on constructing efficiently encodable and decodable codes for the two extreme regimes of high-noise and high-rate. Specifically, we construct polynomial-time decodable codes with the following trade-offs (for any epsilon > 0):

(1) Codes that can correct a fraction 1-epsilon of deletions with rate poly(eps) over an alphabet of size poly(1/epsilon); (2) Binary codes of rate 1-O~(sqrt(epsilon)) that can correct a fraction eps of deletions; and
(3) Binary codes that can be list decoded from a fraction (1/2-epsilon) of deletions with rate poly(epsion)

Our work is the first to achieve the qualitative goals of correcting a deletion fraction approaching 1 over bounded alphabets, and correcting a constant fraction of bit deletions with rate aproaching 1. The above results bring our understanding of deletion code constructions in these regimes to a similar level as worst-case errors.

BibTeX - Entry

@InProceedings{guruswami_et_al:LIPIcs:2015:5341,
  author =	{Venkatesan Guruswami and Carol Wang},
  title =	{{Deletion Codes in the High-noise and High-rate Regimes}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)},
  pages =	{867--880},
  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/2015/5341},
  URN =		{urn:nbn:de:0030-drops-53417},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2015.867},
  annote =	{Keywords: algorithmic coding theory, deletion codes, list decoding, probabilistic method, explicit constructions}
}

Keywords: algorithmic coding theory, deletion codes, list decoding, probabilistic method, explicit constructions
Collection: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)
Issue Date: 2015
Date of publication: 13.08.2015

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