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Brief Announcement: Relaxed Locally Correctable Codes in Computationally Bounded Channels

Authors Jeremiah Blocki, Venkata Gandikota, Elena Grigorescu, Samson Zhou



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Author Details

Jeremiah Blocki
  • Department of Computer Science, Purdue University, West Lafayette, Indiana, USA
Venkata Gandikota
  • Department of Computer Science, Johns Hopkins University, Baltimore, Maryland, USA
Elena Grigorescu
  • Department of Computer Science, Purdue University, West Lafayette, Indiana, USA
Samson Zhou
  • Department of Computer Science, Purdue University, West Lafayette, Indiana, USA

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Jeremiah Blocki, Venkata Gandikota, Elena Grigorescu, and Samson Zhou. Brief Announcement: Relaxed Locally Correctable Codes in Computationally Bounded Channels. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 106:1-106:4, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.ICALP.2018.106

Abstract

We study variants of locally decodable and locally correctable codes in computationally bounded, adversarial channels, under the assumption that collision-resistant hash functions exist, and with no public-key or private-key cryptographic setup. Specifically, we provide constructions of relaxed locally correctable and relaxed locally decodable codes over the binary alphabet, with constant information rate, and poly-logarithmic locality. Our constructions compare favorably with existing schemes built under much stronger cryptographic assumptions, and with their classical analogues in the computationally unbounded, Hamming channel. Our constructions crucially employ collision-resistant hash functions and local expander graphs, extending ideas from recent cryptographic constructions of memory-hard functions.

Subject Classification

ACM Subject Classification
  • Theory of computation → Error-correcting codes
Keywords
  • Relaxed locally correctable codes
  • computationally bounded channels
  • local expanders

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References

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