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We consider a frame asynchronous coded slotted ALOHA (FA-CSA) system foruncoordinated multiple access, where users join the system on a slot-by-slotbasis according to a Poisson random process and, in contrast to standard framesynchronous CSA (FS-CSA), users are not frame-synchronized. We analyze theperformance of FA-CSA in terms of packet loss rate and delay. In particular, wederive the (approximate) density evolution that characterizes the asymptoticperformance of FA-CSA when the frame length goes to infinity. We show that, ifthe receiver can monitor the system before anyone starts transmitting, aboundary effect similar to that of spatially-coupled codes occurs, whichgreatly improves the iterative decoding threshold. Furthermore, we derive tightapproximations of the error floor (EF) for the finite frame length regime,based on the probability of occurrence of the most frequent stopping sets. Weshow that, in general, FA-CSA provides better performance in both the EF andwaterfall regions as compared to FS-CSA. Moreover, FA-CSA exhibits better delayproperties than FS-CSA.

On Frame Asynchronous Coded Slotted ALOHA: Asymptotic, Finite Length, and Delay Analysis