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.2017.43
URN: urn:nbn:de:0030-drops-75922
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7592/
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Frank-Fischer, S. Luna ; Guruswami, Venkatesan ; Wootters, Mary

Locality via Partially Lifted Codes

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Abstract

In error-correcting codes, locality refers to several different ways of quantifying how easily a small amount of information can be recovered from encoded data. In this work, we study a notion of locality called the s-Disjoint-Repair-Group Property (s-DRGP). This notion can interpolate between two very different settings in coding theory: that of Locally Correctable Codes (LCCs) when s is large - a very strong guarantee - and Locally Recoverable Codes (LRCs) when s is small - a relatively weaker guarantee. This motivates the study of the s-DRGP for intermediate s, which is the focus of our paper. We construct codes in this parameter regime which have a higher rate than previously known codes. Our construction is based on a novel variant of the lifted codes of Guo, Kopparty and Sudan. Beyond the results on the s-DRGP, we hope that our construction is of independent interest, and will find uses elsewhere.

BibTeX - Entry

@InProceedings{frankfischer_et_al:LIPIcs:2017:7592,
  author =	{S. Luna Frank-Fischer and Venkatesan Guruswami and Mary Wootters},
  title =	{{Locality via Partially Lifted Codes}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)},
  pages =	{43:1--43:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-044-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{81},
  editor =	{Klaus Jansen and Jos{\'e} D. P. Rolim and David Williamson and Santosh S. Vempala},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7592},
  URN =		{urn:nbn:de:0030-drops-75922},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2017.43},
  annote =	{Keywords: Error correcting codes, locality, lifted codes}
}

Keywords: Error correcting codes, locality, lifted codes
Collection: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)
Issue Date: 2017
Date of publication: 11.08.2017

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