  We consider a frame-asynchronous coded slotted ALOHA (FA-CSA) system where
users become active according to a Poisson random process. In contrast to
standard frame-synchronous CSA (FS-CSA), users transmit a first replica of
their message in the slot following their activation and other replicas
uniformly at random in a number of subsequent slots. We derive the
(approximate) density evolution that characterizes the asymptotic performance
of FA-CSA when the frame length goes to infinity. We show that, if users can
monitor the system before they start transmitting, a boundary-effect similar to
that of spatially-coupled codes occurs, which greatly improves the decoding
threshold as compared to FS-CSA. We also derive analytical approximations of
the error floor (EF) in the finite frame length regime. We show that FA-CSA
yields in general lower EF, better performance in the waterfall region, and
lower average delay, as compared to FS-CSA.
