On formulating a probability of random correspondence of biometrics using error exponents

Performance of biometrics in human authentication can be limited when multiple samples of a user´s biometric information differ due to intra-class variability in acquisition, storage or transmission of biometrics. Thus, random correspondence results between users. We formulate probability of random correspondence (PRC) by developing an information model of biometrics features as a noisy source. The information in features represented by N_s bits inherently has t error bits attributed to the intra-class variabilities. The values of t and bit error probability are shown to be determined from second order statistics of the features. These are used respectively, to formulate information rate of the noisy biometric and to characterize a binary symmetric channel that models the occurrence of errors in a biometric template. Finally, information rate and error probability are combined in the framework of error exponents to formulate PRC of biometrics. We illustrate our approach with simulations, using freely available data, to obtain numerical values of PRC of fingerprint biometrics.