To account for the massive uncoordinated random access scenario, which is relevant for the Internet of Things, Polyanskiy (2017) proposed a novel formulation of the multiple-access problem, commonly referred to as unsourced multiple access, where all users employ a common codebook and the receiver decodes up to a permutation of the messages. We extend this seminal work to the case where the number of active users is random and unknown a priori. We define a random-access code accounting for both misdetection (MD) and false alarm (FA), and derive a random-coding achievability bound for the Gaussian multiple access channel. Our bound captures the fundamental trade-off between MD and FA. It suggests that the lack of knowledge of the number of active users entails a small penalty in energy efficiency when the target MD and FA probabilities are high. However, as the target MD and FA probabilities decrease, the energy efficiency penalty becomes significant. For example, in a typical IoT scenario, the required energy per bit to achieve both MD and FA probabilities below 0.1, predicted by our bound, is only 0.5-0.7 dB higher than that predicted by the bound in Polyanskiy (2017) for a known number of active users. This gap increases to 3-4 dB when the target MD and/or FA probability is 0.001. Taking both MD and FA into account, we use our bound to benchmark the energy efficiency of slotted ALOHA with multi-packet reception, of a decoder that treats interference as noise, and of some recently proposed coding schemes. Numerical results suggest that, when the target MD and FA probabilities are high, it is effective to estimate the number of active users, then treat this estimate as the true value, and use a coding scheme that performs well for the case of known number of active users. However, this approach becomes energy inefficient when the requirements on MD and FA probabilities are stringent.

翻译：为应对物联网场景下大规模非协调随机接入的需求，Polyanskiy (2017) 提出了多址接入问题的新颖表述，通常称为无源多址接入。该方案中所有用户共享同一码本，接收端对消息进行置换解码。我们将这一开创性工作扩展至活跃用户数量随机且先验未知的情形。我们定义了同时考虑漏检（MD）和虚警（FA）的随机接入码，并推导了高斯多址信道的随机编码可达界。该可达界揭示了MD与FA之间的根本折衷关系，表明当目标MD和FA概率较高时，缺乏活跃用户数量信息仅需在能效方面付出微小代价；但随着目标MD和FA概率降低，能效惩罚显著增加。例如，在典型IoT场景中，当目标MD和FA概率均低于0.1时，根据我们的可达界预测，单位比特所需能量仅比Polyanskiy (2017) 中已知活跃用户数的可达界预测值高0.5-0.7 dB；而当目标MD和/或FA概率为0.001时，这一差距扩大至3-4 dB。我们同时考虑了MD与FA，利用该可达界评估了多包接收时隙ALOHA协议、将干扰视为噪声的解码器以及若干近期提出的编码方案的能效性能。数值结果表明，当目标MD和FA概率较高时，先估计活跃用户数再将估计值视为真实值、并采用适用于已知用户数的编码方案较为有效；然而，当MD和FA概率要求严苛时，该方法的能效显著下降。