Document Open Access Logo

On the List Recoverability of Randomly Punctured Codes

Authors Ben Lund , Aditya Potukuchi

PDF

File

Thumbnail PDF
PDF
LIPIcs.APPROX-RANDOM.2020.30.pdf
  • Filesize: 449 kB
  • 11 pages

Document Identifiers

Subject Classification

ACM Subject Classification
  • Theory of computation → Error-correcting codes
Keywords
  • List recovery
  • randomly punctured codes
  • Reed-Solomon codes

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

Abstract

We show that a random puncturing of a code with good distance is list recoverable beyond the Johnson bound. In particular, this implies that there are Reed-Solomon codes that are list recoverable beyond the Johnson bound. It was previously known that there are Reed-Solomon codes that do not have this property. As an immediate corollary to our main theorem, we obtain better degree bounds on unbalanced expanders that come from Reed-Solomon codes.

Cite As Get BibTex

Ben Lund and Aditya Potukuchi. On the List Recoverability of Randomly Punctured Codes. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 176, pp. 30:1-30:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2020.30

Author Details

Ben Lund
  • Department of Mathematics, Princeton University, NJ, USA
Aditya Potukuchi
  • Department of Computer Science, Rutgers University, Piscataway, NJ, USA

Funding

  • Lund, Ben: Research supported by NSF grant DMS-1802787.
  • Potukuchi, Aditya: Research supported in part by Noga Ron-Zewi’s BSF-NSF grant CCF-1814629 and 2017732, by NSF grant CCF-1350572 and the Simons Collaboration on Algorithms and Geometry.

Acknowledgements

We thank Venkat Guruswami, Jeff Kahn, Swastik Kopparty, Noga Ron-Zewi, and Mary Wootters for helpful discussions. We also thank an anonymous reviewer for helpful comments on the presentation of the results.

References

  1. Xue Chen. personal communication. Google Scholar
  2. Xue Chen and David Zuckerman. Existence of simple extractors. Electronic Colloquium on Computational Complexity (ECCC), 25:116, 2018. URL: https://eccc.weizmann.ac.il/report/2018/116.
  3. Devdatt Dubhashi and Alessandro Panconesi. Concentration of Measure for the Analysis of Randomized Algorithms. Cambridge University Press, New York, NY, USA, 1st edition, 2009. Google Scholar
  4. Sivakanth Gopi, Swastik Kopparty, Rafael Mendes de Oliveira, Noga Ron-Zewi, and Shubhangi Saraf. Locally testable and locally correctable codes approaching the Gilbert-Varshamov bound. IEEE Trans. Information Theory, 64(8):5813-5831, 2018. URL: https://doi.org/10.1109/TIT.2018.2809788.
  5. Venkatesan Guruswami. personal communication. Google Scholar
  6. Venkatesan Guruswami. Algorithmic results in list decoding. Foundations and Trends in Theoretical Computer Science, 2(2), 2006. URL: https://doi.org/10.1561/0400000007.
  7. Venkatesan Guruswami and Piotr Indyk. Expander-based constructions of efficiently decodable codes. In Proceedings 42nd IEEE Symposium on Foundations of Computer Science, pages 658-667. IEEE, 2001. Google Scholar
  8. Venkatesan Guruswami and Atri Rudra. Limits to list decoding Reed-Solomon codes. IEEE Trans. Information Theory, 52(8):3642-3649, 2006. URL: https://doi.org/10.1109/TIT.2006.878164.
  9. Venkatesan Guruswami, Christopher Umans, and Salil P. Vadhan. Unbalanced expanders and randomness extractors from parvaresh-vardy codes. J. ACM, 56(4):20:1-20:34, 2009. URL: https://doi.org/10.1145/1538902.1538904.
  10. Atri Rudra and Mary Wootters. Every list-decodable code for high noise has abundant near-optimal rate puncturings. In Symposium on Theory of Computing, STOC 2014, New York, NY, USA, May 31 - June 03, 2014, pages 764-773, 2014. URL: https://doi.org/10.1145/2591796.2591797.
  11. Atri Rudra and Mary Wootters. It'll probably work out: Improved list-decoding through random operations. In Proceedings of the 2015 Conference on Innovations in Theoretical Computer Science, ITCS 2015, Rehovot, Israel, January 11-13, 2015, pages 287-296, 2015. URL: https://doi.org/10.1145/2688073.2688092.
  12. Salil P. Vadhan. The unified theory of pseudorandomness: guest column. SIGACT News, 38(3):39-54, 2007. URL: https://doi.org/10.1145/1324215.1324225.
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact