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Problemy Peredachi Informatsii, 2023, Volume 59, Issue 1, Pages 17–24
DOI: https://doi.org/10.31857/S0555292323010023 (Mi ppi2389) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Coding Theory

Codes for exact support recovery of sparse vectors from inaccurate linear measurements and their decoding

M. Fernandeza, G. A. Kabatianskyb, S. A. Kruglikc, Y. Miaod

a Universitat Politècnica de Catalunya, Barcelona, Spain
b Skolkovo Institute of Science and Technology (Skoltech), Moscow, Russia
c Nanyang Technological University, Singapore
d University of Tsukuba, Tsukuba, Ibaraki, Japan
Full-text PDF (181 kB) First page Citations (5)
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DOI: https://doi.org/10.31857/S0555292323010023
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.
Keywords: compressed sensing, sparse vector support, group testing, false coin problem, signature codes for a noisy multiple-access adder channel, multimedia digital fingerprinting codes.
Funding agency Grant number
Japan Society for the Promotion of Science JPJSBP 120204802
Russian Foundation for Basic Research
Ministerio de Economía y Competitividad de España PID2019-110224RB-I00
Russian Science Foundation 22-41-02028
Ministry of Education, Singapore MOE2019-T2-2-083
MOET2EP20121-000
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.
Received: 30.12.2022
Revised: 21.02.2023
Accepted: 21.02.2023
English version:
Problems of Information Transmission, 2023, Volume 59, Issue 1, Pages 14–21
DOI: https://doi.org/10.1134/S0032946023010027
Bibliographic databases:
Document Type: Article
UDC: 621.391 : 519.72
Language: Russian
Citation: M. Fernandez, G. A. Kabatiansky, S. A. Kruglik, Y. Miao, “Codes for exact support recovery of sparse vectors from inaccurate linear measurements and their decoding”, Probl. Peredachi Inf., 59:1 (2023), 17–24; Problems Inform. Transmission, 59:1 (2023), 14–21
Citation in format AMSBIB
\Bibitem{FerKabKru23}
\by M.~Fernandez, G.~A.~Kabatiansky, S.~A.~Kruglik, Y.~Miao
\paper Codes for exact support recovery of sparse vectors from inaccurate linear measurements and their decoding
\jour Probl. Peredachi Inf.
\yr 2023
\vol 59
\issue 1
\pages 17--24
\mathnet{http://mi.mathnet.ru/ppi2389}
\crossref{https://doi.org/10.31857/S0555292323010023}
\edn{https://elibrary.ru/JDHVDR}
\transl
\jour Problems Inform. Transmission
\yr 2023
\vol 59
\issue 1
\pages 14--21
\crossref{https://doi.org/10.1134/S0032946023010027}
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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