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JOURNALS // Problemy Peredachi Informatsii // Archive

Probl. Peredachi Inf., 2023 Volume 59, Issue 1, Pages 17–24 (Mi ppi2389)

This article is cited in 7 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

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.

UDC: 621.391 : 519.72

Received: 30.12.2022
Revised: 21.02.2023
Accepted: 21.02.2023

DOI: 10.31857/S0555292323010023


 English version:
Problems of Information Transmission, 2023, 59:1, 14–21


© Steklov Math. Inst. of RAS, 2025