Scaling Laws for Many-Access Channels and Unsourced Random Access

In the emerging Internet of Things, a massive number of devices may connect to one common receiver. Consequently, models that study this setting are variants of the classical multiple-access channel where the number of users grows with the blocklength. Roughly, these models can be classified into three groups based on two criteria: the notion of probability of error and whether users use the same codebook. The first group follows the classical notion of probability of error and assumes that users use different codebooks. In the second group, users use different codebooks, but a new notion of probability of error called per-user probability of error is considered. The third group considers the per-user probability of error and that users are restricted to use the same codebook. This group is also known as unsourced random access. For the first and second groups of models, scaling laws that describe the capacity per unit-energy as a function of the order of growth of users were characterized by Ravi and Koch (arxiv.org/abs/2012.10350). In this paper, we first review these results. We then present scaling laws for the third group of models, i.e., unsourced random access.