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.

翻译：在这项研究中,我们调查了生物鉴别识别系统识别、保密、模板和隐私泄漏率之间的基本权衡。Ignatenko和Willems(2015年)研究了这个系统,假设系统注册过程中的频道是无噪音的,他们没有考虑模板率。然而,在注册过程中,人们非常认为,生物数据扫描时会发生噪音。在本文中,我们在注册过程中设置了一个吵闹的频道,并描述利率图普斯的能力区域。能力区域通过两个辅助随机变量的新技术得到了证明,而以前的研究从未见过这两个变量。在特殊案例中,获得的结果显示,特征描述会降低到Ignatenko和Willems(2015年)提供的无噪音频道和模板率不受限制的Ignatenko和Willems(2015年)提供的数据,并且它也与只有一个人的G\"unl\\u"u和Krammer(2018年)得出的结果相吻合。