This work considers an asynchronous $\textsf{K}_\text{a}$-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 $2^{\textsf{K}_\text{a}}-1$ 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：本文考虑一个异步$\textsf{K}_\text{a}$个活跃用户的无源多址接入信道（AUMAC），其中采用最差情况的异步模式。传输消息需在$n$个信道使用内解码完成，但由于异步性，部分码字未能完整接收。我们考虑了最大允许传输延迟的约束条件。AUMAC缺乏同步UMAC的置换不变性，因为具有固定异步性的相同码字的不同置换是可区分的。因此，分析需要计算所有$2^{\textsf{K}_\text{a}}-1$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相应码本。为克服这一挑战，通过研究具有延迟约束的最差异步模式，推导了每用户错误概率（PUPE）的一致界。数值结果表明不同延迟约束下每比特能量与活跃用户数之间的权衡关系。此外，尽管异步传输减少了干扰，但与同步情况相比，由于接收机需用不完整接收的码字进行解码，所需每比特能量有所增加。