Analysis on Reliability Function and Strong Converse of Discrete Memoryless Biometrical Identification Systems

摘要

The biometrical identification system, introduced by Willems et al., is a system to identify individuals based on measurable physical characteristics of each individual. One of the most important factors on this system is the identification capacity, i.e. the maximum achievable rate of the number of individuals that can be distinguished with a vanishing error probability asymptotically. Willems et al. have made clear that the identification capacity of a discrete memory less system can be characterized from an information theoretic perspective. However, in proving the converse theorem, they provided a rigorous proof only for the case where each individual is uniformly distributed to be identified. In this paper, we investigate the reliability function of the system and show that it behaves in the same way as the well-known random coding error exponent. We also provide an explicit proof of the converse part provided that each individual is not uniformly distributed and the identification process is done without the knowledge of the prior distribution. In particular, we use Arimoto's argument to analyze a lower bound on the error probability, which also leads to the proof of the strong converse theorem for a non-uniform prior distribution.