arXiv2023
To account for the massive uncoordinated random access scenario, which is relevant for the Internet of Things, Polyanskiy (2017) proposed a novel formulation of the multiple-access problem, commonly referred to as unsourced multiple access, where all users employ a common codebook and the receiver decodes up to a permutation of the messages. We extend this seminal work to the case where the number of active users is random and unknown a priori. We define a random-access code accounting for both misdetection (MD) and false alarm (FA), and derive a random-coding achievability bound for the Gaussian multiple access channel. Our bound captures the fundamental trade-off between MD and FA. It suggests that the lack of knowledge of the number of active users entails a small penalty in energy efficiency when the target MD and FA probabilities are high. However, as the target MD and FA probabilities decrease, the energy efficiency penalty becomes significant. For example, in a typical IoT scenario, the required energy per bit to achieve both MD and FA probabilities below 0.1, predicted by our bound, is only 0.5-0.7 dB higher than that predicted by the bound in Polyanskiy (2017) for a known number of active users. This gap increases to 3-4 dB when the target MD and/or FA probability is 0.001. Taking both MD and FA into account, we use our bound to benchmark the energy efficiency of slotted ALOHA with multi-packet reception, of a decoder that treats interference as noise, and of some recently proposed coding schemes. Numerical results suggest that, when the target MD and FA probabilities are high, it is effective to estimate the number of active users, then treat this estimate as the true value, and use a coding scheme that performs well for the case of known number of active users. However, this approach becomes energy inefficient when the requirements on MD and FA probabilities are stringent.