Capacity/Storage Tradeoff in High-Dimensional Identification Systems

Abstract

The asymptotic tradeoff between the number of distinguishable objects and the necessary storage space in an identification system is investigated. In the discussed scenario, high-dimensional (and noisy) feature vectors extracted from objects are first compressed and then enrolled in the database. When the user submits a random query object, the extracted noisy feature vector is compared against the compressed entries, one of which is output as the identified object. This paper presents a complete single-letter characterization of achievable storage and identification rates (measured in bits per feature dimension) subject to vanishing probability of identification error as the dimensionality of feature vectors becomes very large.