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