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Polyanskiy 2 proposed a framework for the MAC problem where users employ a common codebook in the finite blocklength regime. In this work, we extend 2 to the case when each user generates a packet independently and asynchronously according to identical renewal processes. Each packet must be decoded with a delay no greater than d, which is a strict delay constraint. We derive a general converse bound for our system model before conducting a comparative analysis of several achievable transmission schemes. First, we consider a transmission scheme where each user transmits a packet as soon as it is generated and suffers interference from other users. We treat interference as noise (TIN). Then, we investigate block transmission where users transmit jointly in fixed slots. Finally, we explore packet splitting, allowing users to divide each packet into two parts with different blocklengths. Using optimized information bit allocation, we discuss two analytical approaches: dependence testing and Gaussian ball. Our numerical results indicate that, when dealing with large delays, TIN performs well compared to block transmission. Conversely, block transmission has the advantage as the system spectral efficiency increases. Packet splitting outperforms other schemes consistently.
Han et al. (Fri,) studied this question.