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On Compressed Sensing of Binary Signals for the Unsourced Random Access Channel.

Elad Romanov¹, Or Ordentlich¹

¹The Rachel and Selim Benin School of Computer Science and Engineering, Hebrew University of Jerusalem, Jerusalem 919050, Israel.

Entropy (Basel, Switzerland)

|June 2, 2021

Summary

This study introduces a new compressed sensing method for binary signals using sparse matrices, achieving performance comparable to dense matrix methods. The approach enables efficient recovery of sparse binary data in unsourced random access applications.

Keywords:

compressed sensing glauber dynamics low-density parity-check codes unsourced random access

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Area of Science:

Signal Processing
Information Theory
Computer Engineering

Background:

Compressed sensing enables signal recovery from fewer measurements than traditional methods.
Binary signal recovery is crucial for applications like unsourced random access.
Existing methods often rely on dense sensing matrices, which can be computationally intensive.

Purpose of the Study:

To develop a novel compressed sensing scheme for binary signals.
To design a sparse sensing matrix and a reliable recovery algorithm.
To improve efficiency and performance in binary signal recovery.

Main Methods:

Designed the sensing matrix (A) using a parity check matrix from a low-density parity-check code (LDPC).
Employed a Markov chain Monte Carlo (MCMC) algorithm for signal recovery.
Leveraged the sparse structure of the LDPC-based sensing matrix for computational speed.

Main Results:

Achieved reliable recovery of sparse binary vectors from noisy measurements (y=Ax+σz).
Demonstrated performance comparable to state-of-the-art schemes using dense sensing matrices.
Showcased the advantages of using a sparse sensing matrix in terms of efficiency.

Conclusions:

The proposed LDPC-based compressed sensing scheme offers a competitive and efficient alternative for binary signal recovery.
This method is particularly beneficial for applications requiring fast and reliable data acquisition, such as unsourced random access.
The use of sparse matrices provides significant practical advantages over dense matrices in compressed sensing.