CHIRRUP: a practical algorithm for unsourced multiple access

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 C=2100 (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 O[nK(log22n+K)]⁠, where n is the codeword length and K is the number of active users. Crucially, the complexity is sublinear in 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.