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Explicit and Efficient Construction of Nearly Optimal Rate Codes for the Binary Deletion Channel and the Poisson Repeat Channel

Author Ittai Rubinstein

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Author Details

Ittai Rubinstein
  • Blavatnik School of Computer Science, Tel-Aviv University, Israel
  • QEDMA Quantum Computing, Tel-Aviv, Israel

Funding

  • Rubinstein, Ittai: The Deutsch institute fund.

Acknowledgements

We thank Roni Con, Aviad Rubinstein and Muli Safra for their helpful comments on previous drafts.

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Ittai Rubinstein. Explicit and Efficient Construction of Nearly Optimal Rate Codes for the Binary Deletion Channel and the Poisson Repeat Channel. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 105:1-105:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.ICALP.2022.105

Abstract

Two of the most common models for channels with synchronisation errors are the Binary Deletion Channel with parameter p (BDC_p) - a channel where every bit of the codeword is deleted i.i.d with probability p, and the Poisson Repeat Channel with parameter λ (PRC_λ) - a channel where every bit of the codeword is repeated Poisson(λ) times.
Previous constructions based on synchronisation strings yielded codes with rates far lower than the capacities of these channels [Con and Shpilka, 2019; Guruswami and Li, 2018], and the only efficient construction to achieve capacity on the BDC at the time of writing this paper is based on the far more advanced methods of polar codes [Tal et al., 2021].
In this work, we present a new method for concatenating synchronisation codes and use it to construct simple and efficient encoding and decoding algorithms for both channels with nearly optimal rates.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Coding theory
Keywords
  • Error Correcting Codes
  • Algorithmic Coding Theory
  • Binary Deletion Channel

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