Relaxed Locally Correctable Codes in Computationally Bounded Channels

Jeremiah Blocki, Venkata Gandikota, Elena Grigorescu, Samson Zhou

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Error-correcting codes that admit local decoding and correcting algorithms have been the focus of much recent research due to their numerous applications. An important goal is to obtain the best possible tradeoffs between the number of symbols of the codeword that the local decoding algorithm must examine (the locality of the task), and the amount of redundancy in the encoding (the information rate).In Hamming's classical adversarial channel model, the current tradeoffs are dramatic, allowing either small locality, but superpolynomial blocklength, or small blocklength, but high locality. However, in the computationally bounded, adversarial channel model, proposed by Lipton (STACS 1994), constructions of locally decodable codes suddenly exhibit small locality and small blocklength, but these constructions require strong trusted setup assumptions e.g., Ostrovsky, Pandey and Sahai (ICALP 2007) construct private locally decodable codes in the setting where the sender and receiver already share a symmetric key.We study variants of locally decodable and locally correctable codes in computationally bounded, adversarial channels, in a setting with no public-key or private-key cryptographic setup. The only setup assumption we require is the selection of the public parameters (seed) for a collision-resistant hash function. 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, which compare favorably with their classical analogs, crucially employ collision-resistant hash functions and local expander graphs, extending ideas from recent cryptographic constructions of memory-hard functions.

Original languageEnglish (US)
Title of host publication2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2414-2418
Number of pages5
ISBN (Electronic)9781538692912
DOIs
StatePublished - Jul 2019
Externally publishedYes
Event2019 IEEE International Symposium on Information Theory, ISIT 2019 - Paris, France
Duration: Jul 7 2019Jul 12 2019

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2019-July
ISSN (Print)2157-8095

Conference

Conference2019 IEEE International Symposium on Information Theory, ISIT 2019
CountryFrance
CityParis
Period7/7/197/12/19

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics

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