Encyclopedia of Algorithms

2016 Edition
| Editors: Ming-Yang Kao

Locally Decodable Codes

  • Shubhangi SarafEmail author
Reference work entry
DOI: https://doi.org/10.1007/978-1-4939-2864-4_708

Years and Authors of Summarized Original Work

  • 2000; Katz, Trevisan

  • 2002; Goldreich, Karloff, Schulman, Trevisan

  • 2004; Kerenedis, de Wolf

  • 2007; Woodruff

  • 2007; Raghavendra

  • 2008; Yekhanin

  • 2009; Efremenko

  • 2010; Dvir, Gopalan, Yekhanin

  • 2010; Woodruff

  • 2011; Kopparty, Saraf, Yekhanin

  • 2013; Hemenway, Ostrovsky, Wootters

  • 2013; Guo, Kopparty, Sudan

  • 2015; Kopparty, Meir, Ron-Zewi, Saraf

Problem Definition

Classical error-correcting codes allow one to encode a k-bit message x into an n-bit codeword C(x), in such a way that x can still be accurately recovered even if C(x) gets corrupted in a small number of coordinates. The traditional way to recover even a small amount of information contained in x from a corrupted version of C(x) is to run a traditional decoder for C, which would read and process the entire corrupted codeword, to recover the entire original message x. The required information or required piece of xcan then be read off. In the current digital age where huge amounts of data need...

Keywords

Error correcting codes Locally decodable codes Sublinear time algorithms 
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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Mathematics and Department of Computer Science, Rutgers UniversityPiscatawayUSA