  In this study, we investigate fundamental trade-off among identification,
secrecy, template, and privacy-leakage rates in biometric identification
systems. Ignatenko and Willems (2015) studied this system assuming that the
channel in the enrollment process of the system is noiseless and they did not
consider the template rate. In the enrollment process, however, it is highly
considered that noise occurs when bio-data is scanned. In this paper, we impose
a noisy channel in the enrollment process and characterize the capacity region
of the rate tuples. The capacity region is proved by a novel technique via two
auxiliary random variables, which has never been seen in previous studies. As
special cases, the obtained result shows that the characterization reduces to
the one given by Ignatenko and Willems (2015) where the enrollment channel is
noiseless and there is no constraint on the template rate, and it also
coincides with the result derived by G\"unl\"u and Kramer (2018) where there is
only one individual.
