A New Characterization of the Capacity Region of Identification Systems Under Noisy Enrollment

The fundamental limits of two common models: generated and chosen secret models in biometric identification systems with exponentially many users are considered. Recently, Yachongka and Yagi (2019) characterized the capacity region among identification, secrecy, template, and privacy-leakage rates for the generated secret model via two auxiliary random variables. In this study, we provide an alternative characterization of the capacity regions of these rates for the generated secret model by a single auxiliary random variable. Compared to the proof approach in the previous study, the basic idea is that we have changed the achievability scheme, which fits the technique employing only one auxiliary random variable, and introduce a partial decoder, estimating only the secret key of users, to deal with evaluating the privacy-leakage rate in the achievability proof. We further apply the proof method of the generated secret model to characterize the capacity region for the chosen secret model. As special cases, the characterizations naturally reduce to the result given by Ignatenko and Willems (2015) when the enrollment channel is noiseless and there is no constraint on the template rate, and also correspond to the result given by Günlü and Kramer (2018) when there is only one user.