Motivated by the need to provide differentiated quality-of-service (QoS) in grant-free uplink transmissions in 5G networks and beyond, we extend the probabilistic analysis of coded Poisson receivers (CPR) to the setting with multiple classes of users and receivers. For such a CPR system, we prove (under certain technical conditions) that there is a region, called the stability region in this paper. Each transmitted packet can be successfully received with probability 1 when the offered load to the system is within the stability region. On the other hand, if the offered load is outside the stability region, there is a nonzero probability that a packet will fail to be received. We then extend the stability region to the $\epsilon$-stability region for CPR systems with decoding errors. We also demonstrate the capability of providing differentiated QoS in such CPR systems by comparing the stability regions under various parameter settings.

中文翻译：

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具有多类用户和接收器的编码泊松接收器的稳定域

由于需要在 5G 网络及以后的无授权上行链路传输中提供差异化​​的服务质量 (QoS)，我们将编码泊松接收器 (CPR) 的概率分析扩展到具有多类用户和接收器的设置。对于这样的CPR系统，我们证明（在一定技术条件下）存在一个区域，本文称为稳定区域。当提供给系统的负载在稳定区域内时，每个传输的数据包可以成功接收的概率为 1。另一方面，如果提供的负载在稳定区域之外，则数据包接收失败的概率非零。然后，我们将稳定性区域扩展到具有解码错误的 CPR 系统的 $\epsilon$-稳定区域。