  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.
