  Unsourced random access (URA) is a recently proposed communication paradigm
attuned to machine-driven data transfers. In the original URA formulation, all
the active devices share the same number of bits per packet. The scenario where
several classes of devices transmit concurrently has so far received little
attention. An initial solution to this problem takes the form of group
successive interference cancellation, where codewords from a class of devices
with more resources are recovered first, followed by the decoding of the
remaining messages. This article introduces a joint iterative decoding approach
rooted in approximate message passing. This framework has a concatenated coding
structure borrowed from the single-class coded compressed sensing and admits a
solution that offers performance improvement at little added computational
complexity. Our findings point to new connections between multi-class URA and
compressive demixing. The performance of the envisioned algorithm is validated
through numerical simulations.
