  Sparse regression codes with approximate message passing (AMP) decoding have
gained much attention in recent times. The concepts underlying this coding
scheme extend to unsourced random access with coded compressed sensing (CCS),
as first demonstrated by Fengler, Jung, and Caire. Specifically, their approach
employs a concatenated coding framework with an inner AMP decoder followed by
an outer tree decoder. In their original implementation, these two components
work independently of each other, with the tree decoder acting on the static
output of the AMP decoder. This article introduces a novel framework where the
inner AMP decoder and the outer tree decoder operate in tandem, dynamically
passing information back and forth to take full advantage of the underlying CCS
structure. This scheme necessitates the redesign of the tree code as to enable
belief propagation in a computationally tractable manner. The enhanced
architecture exhibits significant performance benefits over a range of system
parameters. The error performance of the proposed scheme can be accurately
predicted through a set of equations, known as state evolution of AMP. These
findings are supported both analytically and through numerical methods.
