Asymptotic and finite frame length analysis of frame asynchronous coded slotted ALOHA

We consider a frame-asynchronous coded slotted ALOHA (FA-CSA) system where users join according to a Poisson random process. In contrast to standard frame-synchronous CSA (FS-CSA), when a user joins the system, it transmits a first replica of its message in the following slot 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 the receiver can monitor the system before users 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.