Relaxed Locally Correctable Codes in Computationally Bounded Channels

Jeremiah Blocki, Venkata Gandikota, Elena Grigorescu, Samson Zhou

Research output: Contribution to journalArticlepeer-review

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), 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. We study variants of locally decodable and locally correctable codes in computationally bounded, adversarial channels, in a setting with no trusted setup. The only 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 polylogarithmic 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)
JournalIEEE Transactions on Information Theory
DOIs
StateAccepted/In press - 2021

Keywords

  • Complexity theory
  • Decoding
  • Depth-robust graphs
  • Encoding
  • Error analysis
  • Indexes
  • Local codes
  • Probabilistic logic
  • Receivers

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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