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Rate Amplification and Query-Efficient Distance Amplification for Linear LCC and LDC

Authors Gil Cohen, Tal Yankovitz

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

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Abstract

The main contribution of this work is a rate amplification procedure for LCC. Our procedure converts any q-query linear LCC, having rate ρ and, say, constant distance to an asymptotically good LCC with q^poly(1/ρ) queries.
Our second contribution is a distance amplification procedure for LDC that converts any linear LDC with distance δ and, say, constant rate to an asymptotically good LDC. The query complexity only suffers a multiplicative overhead that is roughly equal to the query complexity of a length 1/δ asymptotically good LDC. This improves upon the poly(1/δ) overhead obtained by the AEL distance amplification procedure [Alon and Luby, 1996; Alon et al., 1995].
Our work establishes that the construction of asymptotically good LDC and LCC is reduced, with a minor overhead in query complexity, to the problem of constructing a vanishing rate linear LCC and a (rapidly) vanishing distance linear LDC, respectively.

Cite As Get BibTex

Gil Cohen and Tal Yankovitz. Rate Amplification and Query-Efficient Distance Amplification for Linear LCC and LDC. In 36th Computational Complexity Conference (CCC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 200, pp. 1:1-1:57, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.CCC.2021.1

Author Details

Gil Cohen
  • Department of Computer Science, Tel Aviv University, Israel
Tal Yankovitz
  • Department of Computer Science, Tel Aviv University, Israel

Funding

The research leading to these results has received funding from the ERC starting grant 949499, the Israel Science Foundation grant 1569/18 and from the Azrieli Faculty Fellowship.

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