This work considers an asynchronous $\textsf{K}_a$-active-user unsourced multiple access channel (AUMAC) with the worst-case asynchronicity. The transmitted messages must be decoded within $n$ channel uses, while some codewords are not completely received due to asynchronicities. We consider a constraint of the largest allowed delay of the transmission. The AUMAC lacks the permutation-invariant property of the synchronous UMAC since different permutations of the same codewords with a fixed asynchronicity are distinguishable. Hence, the analyses require calculating all $2^{\textsf{K}_a}-1$ combinations of erroneously decoded messages. Moreover, transmitters cannot adapt the corresponding codebooks according to asynchronicity due to a lack of information on asynchronicities. To overcome this challenge, a uniform bound of the per-user probability of error (PUPE) is derived by investigating the worst-case of the asynchronous patterns with the delay constraint. Numerical results show the trade-off between the energy-per-bit and the number of active users for different delay constraints. In addition, although the asynchronous transmission reduces interference, the required energy-per-bit increases as the receiver decodes with incompletely received codewords, compared to the synchronous case.

翻译：本文考虑一种具有最坏异步特性的 $\textsf{K}_a$ 活跃用户无源多址接入信道（AUMUC）。传输消息需在 $n$ 个信道使用内解码，但由于异步性，部分码字未能完全接收。我们针对最大允许传输延迟施加了约束。与同步UMAC不同，AUMUC不具备置换不变性，因为固定异步性下同一码字的不同置换是可区分的。因此，分析需要计算所有 $2^{\textsf{K}_a}-1$ 种错误解码消息的组合。此外，由于缺乏异步性信息，发射机无法根据异步性调整对应码本。为克服此挑战，通过研究具有延迟约束的最坏异步模式，推导了每用户错误概率（PUPE）的统一界。数值结果显示了不同延迟约束下每比特能量与活跃用户数之间的权衡。此外，尽管异步传输减少了干扰，但与同步情况相比，由于接收机需解码未完全接收的码字，所需的每比特能量会增加。