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.

翻译：本文提出了一种卷积编码泊松接收机（CCPRs）的框架，该框架将空间耦合方法融入编码泊松接收机（CPRs）架构。我们利用密度演化方程追踪采用连续干扰消除（SIC）技术的分组解码过程。当底层信道可用$\phi$-ALOHA接收机建模时，我们推导了CPRs稳定区的外界。稳定区是使每个分组能以概率1成功接收的负载集合。我们的外界推广了空间耦合不规则重复时隙ALOHA（IRSA）协议的相关结论，并适用于多业务类别的信道模型。对于单用户类别的CCPRs，稳定区退化为一个区间，因而可用逾渗阈值刻画。我们通过构建CCPR的基础CPR的势函数研究该势阈值。此外，我们证明在窗口大小的技术条件下CCPR是稳定的。针对多类别场景，我们递归评估密度演化方程以确定稳定区的边界。数值结果表明，通过利用空间耦合方法，CCPRs的稳定区相较于CPRs可被扩大。当窗口尺寸较大时，CCPRs的稳定区接近我们的外界。