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

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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 ℓp-norm bounded from above. We propose a decoding algorithm with asymptotically minimum complexity.

About the authors

Marcel Fernandez

Universitat Politicnica de Catalunya

Email: marcelf@entel.upc.edu
Barcelona, Spain

G. A Kabatiansky

Skolkovo Institute of Science and Technology (Skoltech)

Email: g.kabatyansky@skoltech.ru
Moscow, Russia

S. A Kruglik

Nanyang Technological University

Email: stanislav.kruglik@ntu.edu.sg
Singapore

Ying Miao

University of Tsukuba

Email: miao@sk.tsukuba.ac.jp
Tsukuba, Ibaraki, Japan

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