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On Compressed Sensing of Binary Signals for the Unsourced Random Access Channel
- Source :
- Entropy 23.5 (2021): 605
- Publication Year :
- 2021
-
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 $\mathbf{x}$ can be recovered reliably from the measurements $\mathbf{y}=A\mathbf{x}+\sigma\mathbf{z}$, where $\mathbf{z}$ 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 $\mathbf{x}$ from the measurements $\mathbf{y}$ 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.<br />Comment: Accepted to Entropy Special Issue on "Information-Theoretic Aspects of Non-Orthogonal and Massive Access for Future Wireless Networks"
Details
- Database :
- arXiv
- Journal :
- Entropy 23.5 (2021): 605
- Publication Type :
- Report
- Accession number :
- edsarx.2105.05350
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.3390/e23050605