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Codes for Exact Support Recovery of Sparse Vectors from Inaccurate Linear Measurements and Their Decoding

  • CODING THEORY
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Abstract

We construct codes that allow to exactly recover the support of an unknown sparse vector with almost equal absolute values of all nonzero coordinates given results of linear measurements in the presence of noise with \(\ell_p\)-norm bounded from above. We propose a decoding algorithm with asymptotically minimum complexity.

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Funding

The research of M. Fernandez was partially supported by the Spanish Government Grant TCO-RISEBLOCK, no. PID2019-110224RB-I00, project MINECO. The research of G.A. Kabatiansky was carried out at the expense of the Russian Science Foundation, project no. 22-41-02028. The research of S.A. Kruglik was partially supported by the Ministry of Education of Singapore, Academic Research Fund Tier 2 Grants MOE2019-T2-2-083 and MOE-T2EP20121-0007. The research of Y. Miao was partially supported by the joint Japan–Russia Research Cooperative Program between the Japan Society for the Promotion of Science and the Russian Foundation for Basic Research under project no. JPJSBP120204802.

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Authors and Affiliations

  1. Universitat Politècnica de Catalunya, Barcelona, Spain

    M. Fernandez

  2. Skolkovo Institute of Science and Technology (Skoltech), Moscow, Russia

    G. A. Kabatiansky

  3. Nanyang Technological University, Singapore, Singapore

    S. A. Kruglik

  4. University of Tsukuba, Tsukuba, Ibaraki, Japan

    Y. Miao

Authors
  1. M. Fernandez
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  2. G. A. Kabatiansky
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  3. S. A. Kruglik
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  4. Y. Miao
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Additional information

Translated from Problemy Peredachi Informatsii, 2023, Vol. 59, No. 1, pp. 17–24. https://doi.org/10.31857/S0555292323010023

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Fernandez, M., Kabatiansky, G.A., Kruglik, S.A. et al. Codes for Exact Support Recovery of Sparse Vectors from Inaccurate Linear Measurements and Their Decoding. Probl Inf Transm 59, 14–21 (2023). https://doi.org/10.1134/S0032946023010027

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  • DOI: https://doi.org/10.1134/S0032946023010027

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