## 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 language | American English |
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Article number | 605 |

Journal | Entropy |

Volume | 23 |

Issue number | 5 |

DOIs | |

State | Published - 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