On compressed sensing of binary signals for the unsourced random access channel

Elad Romanov, Or Ordentlich*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

Motivated by applications in unsourced random access, this paper develops a novel scheme for the problem of compressed sensing of binary signals. In this problem, the goal is to design a sensing matrix A and a recovery algorithm, such that the sparse binary vector x can be recovered reliably from the measurements y = Ax + σz, where z is additive white Gaussian noise. We propose to design A as a parity check matrix of a low-density parity-check code (LDPC) and to recover x from the measurements y using a Markov chain Monte Carlo algorithm, which runs relatively fast due to the sparse structure of A. The performance of our scheme is comparable to state-of-the-art schemes, which use dense sensing matrices, while enjoying the advantages of using a sparse sensing matrix.

Original languageAmerican English
Article number605
JournalEntropy
Volume23
Issue number5
DOIs
StatePublished - 14 May 2021

Bibliographical note

Publisher Copyright:
© 2021 by the authors. Licensee MDPI, Basel, Switzerland.

Keywords

  • Compressed sensing
  • Glauber dynamics
  • Low-density parity-check codes
  • Unsourced random access

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