A New Biometric Identification Model and the Multiple Hypothesis Testing for Arbitrarily Varying Objects

We introduce a new interpretation for the biometric enrollment and identification paradigms and show how the problem of multiple hypothesis testing (HT) for arbitrarily varying sources (AVS) in a special case relates to it. The traditional studies on biometric systems from communication perspectives assume the noisy channel model. If suppose that the process of the biometric data enrollment for a person can be performed several times and at each time both the person and the detector have some arbitrary “state”, then those observations characterized according to their empirical distributions can be treated as family distributions of an AVS. It means that M persons enrollment indicate M different AVS’s. Then the problem of biometric identification based on a new observation turns to be a detection of true AVS with an additional option of rejecting the existing M hypotheses. In this context, the biometric identification over noisy channels converts to one in an arbitrarily varying stochastic environment. We consider the problem within a fundamental framework of HT and information theory. The asymptotic tradeoffs among error probability exponents associated with false acceptance of rejection decision and false rejection of true distribution family are investigated and the optimal decision strategies are outlined. It is proved that for an optimal discrimination of M hypothetical distribution families/persons the ideal detector permits always lower error than in deciding in favor of the rejection.