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Locally Decodable/Correctable Codes for Insertions and Deletions

Authors Alexander R. Block, Jeremiah Blocki, Elena Grigorescu, Shubhang Kulkarni, Minshen Zhu

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Author Details

Alexander R. Block
  • Purdue University, West Lafayette, IN, USA
Jeremiah Blocki
  • Purdue University, West Lafayette, IN, USA
Elena Grigorescu
  • Purdue University, West Lafayette, IN, USA
Shubhang Kulkarni
  • University of Illinois Urbana-Champaign, IL, USA
Minshen Zhu
  • Purdue University, West Lafayette, IN, USA

Funding

  • Block, Alexander R.: Supported by NSF CCF-1910659.
  • Blocki, Jeremiah: Supported by NSF CCF-1910659, CNS-1755708, CNS-1704587 and CNS-1931443.
  • Grigorescu, Elena: Supported by NSF CCF-1910659 and NSF CCF-1910411.
  • Zhu, Minshen: Supported by NSF CCF-1910659.

Cite As Get BibTex

Alexander R. Block, Jeremiah Blocki, Elena Grigorescu, Shubhang Kulkarni, and Minshen Zhu. Locally Decodable/Correctable Codes for Insertions and Deletions. In 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 182, pp. 16:1-16:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.FSTTCS.2020.16

Abstract

Recent efforts in coding theory have focused on building codes for insertions and deletions, called insdel codes, with optimal trade-offs between their redundancy and their error-correction capabilities, as well as efficient encoding and decoding algorithms.
In many applications, polynomial running time may still be prohibitively expensive, which has motivated the study of codes with super-efficient decoding algorithms. These have led to the well-studied notions of Locally Decodable Codes (LDCs) and Locally Correctable Codes (LCCs). Inspired by these notions, Ostrovsky and Paskin-Cherniavsky (Information Theoretic Security, 2015) generalized Hamming LDCs to insertions and deletions. To the best of our knowledge, these are the only known results that study the analogues of Hamming LDCs in channels performing insertions and deletions.
Here we continue the study of insdel codes that admit local algorithms. Specifically, we reprove the results of Ostrovsky and Paskin-Cherniavsky for insdel LDCs using a different set of techniques. We also observe that the techniques extend to constructions of LCCs. Specifically, we obtain insdel LDCs and LCCs from their Hamming LDCs and LCCs analogues, respectively. The rate and error-correction capability blow up only by a constant factor, while the query complexity blows up by a poly log factor in the block length.
Since insdel locally decodable/correctble codes are scarcely studied in the literature, we believe our results and techniques may lead to further research. In particular, we conjecture that constant-query insdel LDCs/LCCs do not exist.

Subject Classification

ACM Subject Classification
  • Theory of computation → Error-correcting codes
Keywords
  • Locally decodable/correctable codes
  • insert-delete channel

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