CHIRRUP: a practical algorithm for unsourced multiple access

Abstract

Abstract Unsourced multiple access abstracts grantless simultaneous communication of a large number of devices (messages) each of which transmits (is transmitted) infrequently. It provides a model for machine-to-machine communication in the Internet of Things, including the special case of radio-frequency identification, as well as neighbour discovery in ad hoc wireless networks. This paper presents a fast algorithm for unsourced multiple access that scales to ${\mathscr{C}}=2^{100}$ (active or non-active) devices (arbitrary $100$ bit messages). The primary building block is multiuser detection of binary chirps, which are simply codewords in the second-order Reed–Muller code. The chirp detection algorithm originally presented by Howard et al. (2008, 42nd Annual Conference on Information Sciences and Systems) is enhanced and integrated into a peeling decoder designed for a patching and slotting framework. In terms of both energy per bit and number of active devices (number of transmitted messages), the proposed algorithm is within a factor of $2$ of state-of-the-art approaches. A significant advantage of our algorithm is its computational efficiency. We prove that the worst-case complexity of the basic chirp reconstruction algorithm is ${\mathscr{O}}[nK(\log _2^2 n + K)]$, where $n$ is the codeword length and $K$ is the number of active users. Crucially, the complexity is sublinear in ${\mathscr{C}}$, which makes the reconstruction computationally feasible—a claim we support by reporting computing times for our algorithm. Our performance and computing time results represent a benchmark against which other practical algorithms can be measured.