  This article seeks to advance coded compressed sensing (CCS) as a practical
scheme for unsourced random access. The original CCS algorithm features a
concatenated structure where an inner code is tasked with support recovery, and
an outer tree code conducts message disambiguation. Recently, a link between
CCS and sparse regression codes was established, leading to the application of
approximate message passing (AMP) to CCS. This connection was subsequently
strengthened by integrating AMP and belief propagation on the outer code
through a dynamic denoiser. Along these lines, this work shows how block
diagonal sensing matrices akin to those used in traditional CCS, together with
the aforementioned dynamic denoiser, form an effective means to get good
performance at low-complexity. This novel architecture can be used to scale
this scheme to dimensions that were previously impractical. Findings are
supported by numerical simulations.
