Reliability Function and Strong Converse of Biometrical Identification Systems Based on List-Decoding

Hideki YAGI

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E100-A    No.5    pp.1262-1266
Publication Date: 2017/05/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E100.A.1262
Type of Manuscript: LETTER
Category: Information Theory
biometrical identification system,  identification capacity,  error probability,  reliability function,  strong converse,  

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The biometrical identification system, introduced by Willems et al., is a system to identify individuals based on their measurable physical characteristics. Willems et al. characterized the identification capacity of a discrete memoryless biometrical identification system from information theoretic perspectives. Recently, Mori et al. have extended this scenario to list-decoding whose list size is an exponential function of the data length. However, as the data length increases, how the maximum identification error probability (IEP) behaves for a given rate has not yet been characterized for list-decoding. In this letter, we investigate the reliability function of the system under fixed-size list-decoding, which is the optimal exponential behavior of the maximum IEP. We then use Arimoto's argument to analyze a lower bound on the maximum IEP with list-decoding when the rate exceeds the capacity, which leads to the strong converse theorem. All results are derived under the condition that an unknown individual need not be uniformly distributed and the identification process is done without the knowledge of the prior distribution.