Reliability function and strong converse of biometrical identification systems

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 memoryless system can be characterized from an information theoretic perspective. Recently, Mori et al. have extended this scenario and characterized the identification capacity under list-decoding whose list size is an exponential function of the data length. However, as the length of biometrical data sequences increases, how the maximum identification error probability of the system behaves; that is, how fast it decreases for a given rate, has not yet been discussed. In this paper, we first use Arimoto's argument to analyze a lower bound on the error probability, which leads to the proof of the strong converse theorem when each individual is not uniformly distributed and the identification process is done without the knowledge of the prior distribution. We then investigate the reliability function of the system under fixed-size list-decoding, which is the optimal exponential behavior of the maximum identification error probability, and it is shown that the reliability function behaves like the well-known random coding error exponent.