Irregular repetition slotted Aloha (IRSA) has shown significant advantages as a modern technique for uncoordinated random access with massive number of users due to its capability of achieving theoretically a throughput of $1$ packet per slot. When the receiver has also the multi-packet reception of multi-user (MUD) detection property, by applying successive interference cancellation, IRSA also obtains very low packet loss probabilities at low traffic loads, but is unable in general to achieve a normalized throughput close to the $1$. In this paper, we reconsider the case of IRSA with $k$-MUD receivers and derive the general density evolution equations for the non-asymptotic analysis of the packet loss rate, for arbitrary frame lengths and two variants of the first slot used for transmission. Next, using the potential function, we give new capacity bounds on the capacity of the system, showing the threshold arrival rate for zero decoding error probability. Our numerical results illustrate performance in terms of throughput and average delay for $k$-MUD IRSA with finite memory at the receiver, and also with bounded maximum delay.

翻译：不规则重复时隙ALOHA（IRSA）作为面向海量用户的无协调随机接入现代技术，因理论上可实现每时隙传输1个数据包的通量而展现出显著优势。当接收端同时具备多用户检测（MUD）的多包接收特性时，通过应用连续干扰消除，IRSA在低业务负载下可获得极低的丢包概率，但通常无法实现接近1的归一化吞吐量。本文重新研究了配备k-MUD接收机的IRSA场景，针对任意帧长及传输初始时隙的两种变体，推导了用于丢包率非渐近分析的一般性密度演化方程。进而借助势函数，给出了系统容量的新界值，揭示了实现零解码错误概率的阈值到达率。数值结果展示了具有接收端有限存储及有界最大延迟的k-MUD IRSA系统在吞吐量和平均时延方面的性能表现。