Numerous applications in the field of molecular communications (MC) such as healthcare systems are often event-driven. The conventional Shannon capacity may not be the appropriate metric for assessing performance in such cases. We propose the identification (ID) capacity as an alternative metric. Particularly, we consider randomized identification (RI) over the discrete-time Poisson channel (DTPC), which is typically used as a model for MC systems that utilize molecule-counting receivers. In the ID paradigm, the receiver's focus is not on decoding the message sent. However, he wants to determine whether a message of particular significance to him has been sent or not. In contrast to Shannon transmission codes, the size of ID codes for a Discrete Memoryless Channel (DMC) grows doubly exponentially fast with the blocklength, if randomized encoding is used. In this paper, we derive the capacity formula for RI over the DTPC subject to some peak and average power constraints. Furthermore, we analyze the case of state-dependent DTPC.

翻译：分子通信（MC）领域中的众多应用（如医疗健康系统）通常具有事件驱动特性。在此类场景中，传统的香农容量可能并非评估性能的合适指标。我们提出将辨识（ID）容量作为替代指标。具体而言，我们考虑离散时间泊松信道（DTPC）上的随机化辨识（RI），该信道通常被用作采用分子计数接收器的MC系统模型。在ID范式中，接收机的重点并非解码所发送的消息，而是希望判断某个对其具有特定意义的消息是否被发送。与香农传输码不同，若采用随机化编码，离散无记忆信道（DMC）的ID码码本规模随码块长度呈双重指数增长。本文推导了在峰值与平均功率约束下DTPC上RI的容量公式，并进一步分析了状态相关DTPC的情形。