Uncertainty in Identification Systems

We study the high-dimensional identification systems under the presence of statistical uncertainties. The task is to design mappings for enrollment and identification purposes. The identification mapping compresses users' information then stores the index in the corresponding position in a database. The identification mapping combines the information in the database and the observation which originates randomly from an enrolled user to produce an estimate of the underlying user index. We study two scenarios. Users' data are generated from the same unknown distribution while the observation channel is also subjected to uncertainty. Each user's data are generated iid from the distribution corresponding to its own state, while the observation channel is known. We provide an achievable compression-identification trade-off for the first and second settings considering both discrete and continuous cases. In the discrete scenario, the described regions are also the correspondingly complete characterizations.