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List-Decodability of Structured Ensembles of Codes (Invited Talk)

Author Mary Wootters

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Mary Wootters
  • Stanford University, CA, USA

Acknowledgements

This invited talk is based on the work [Guruswami et al., 2020], co-authored with Jonathan Mosheiff, Nicolas Resch, Noga Ron-Zewi, and Shashwat Silas; and on the work [Mosheiff et al., 2019], co-authored with Venkatesan Guruswami, Ray Li, Jonathan Mosheiff, Nicolas Resch, and Shashwat Silas.

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Mary Wootters. List-Decodability of Structured Ensembles of Codes (Invited Talk). In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 3:1-3:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.MFCS.2020.3

Abstract

What combinatorial properties are satisfied by a random subspace over a finite field? For example, is it likely that not too many points lie in any Hamming ball? What about any cube? In this talk, I will discuss the answer to these questions, along with a more general characterization of the properties that are likely to be satisfied by a random subspace. The motivation for this characterization comes from error correcting codes. I will discuss how to use this characterization to make progress on the questions of list-decoding and list-recovery for random linear codes, and also to establish the list-decodability of random Low Density Parity-Check (LDPC) codes.
This talk is based on the works [Mosheiff et al., 2019] and [Guruswami et al., 2020], which are joint works with Venkatesan Guruswami, Ray Li, Jonathan Mosheiff, Nicolas Resch, Noga Ron-Zewi, and Shashwat Silas.

Subject Classification

ACM Subject Classification
  • Theory of computation → Error-correcting codes
Keywords
  • Error Correcting Codes
  • List-Decoding

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References

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