  In this paper, we present a framework for convolutional coded Poisson
receivers (CCPRs) that incorporates spatially coupled methods into the
architecture of coded Poisson receivers (CPRs). We use density evolution
equations to track the packet decoding process with the successive interference
cancellation (SIC) technique. We derive outer bounds for the stability region
of CPRs when the underlying channel can be modeled by a $\phi$-ALOHA receiver.
The stability region is the set of loads that every packet can be successfully
received with a probability of 1. Our outer bounds extend those of the
spatially-coupled Irregular Repetition Slotted ALOHA (IRSA) protocol and apply
to channel models with multiple traffic classes. For CCPRs with a single class
of users, the stability region is reduced to an interval. Therefore, it can be
characterized by a percolation threshold. We study the potential threshold by
the potential function of the base CPR used for constructing a CCPR. In
addition, we prove that the CCPR is stable under a technical condition for the
window size. For the multiclass scenario, we recursively evaluate the density
evolution equations to determine the boundaries of the stability region.
Numerical results demonstrate that the stability region of CCPRs can be
enlarged compared to that of CPRs by leveraging the spatially-coupled method.
Moreover, the stability region of CCPRs is close to our outer bounds when the
window size is large.
