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 can be recovered reliably from the measurements , where 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 from the measurements 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.
Highlights
IntroductionThe emergence of the Internet of Things (IoT) has motivated much research interest in designing communication protocols for massive machine-to-machine type communication
The emergence of the Internet of Things (IoT) has motivated much research interest in designing communication protocols for massive machine-to-machine type communication.This type of communication setup is characterized by a large number of users that transmit simultaneously to the same receiver, while each of these users has a very short message to send
The performance of a communication scheme over the unsourced random access channel is assessed by the tradeoff it achieves between energy-per-bit and the per-user probability of error (PUPE), which is the probability that the message transmitted by an active user did not enter the list of messages the receiver outputs
Summary
The emergence of the Internet of Things (IoT) has motivated much research interest in designing communication protocols for massive machine-to-machine type communication This type of communication setup is characterized by a large number of users that transmit simultaneously to the same receiver, while each of these users has a very short message to send. In [1], Polyanskiy defined a communication model capturing the challenges in massive machine-to-machine type communication In this model, there is an unbounded number of potential users, among which only k are active at each frame. The receiver’s goal is to recover a list of k messages that contains “most” of the transmitted messages, without identifying the sender of each message This setup is called the unsourced random access channel [2]. The performance of a communication scheme over the unsourced random access channel is assessed by the tradeoff it achieves between energy-per-bit and the per-user probability of error (PUPE), which is the probability that the message transmitted by an active user did not enter the list of messages the receiver outputs
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