Identification Rates for Block-correlated Gaussian Sources

Among many current data processing systems, the objectives are often not the reproduction of data, but to compute some answers based on the data responding to some queries. The similarity identification task is to identify the items in a database which are similar to a given query item regarding to a certain metric. The problem of compression for similarity identification has been studied in [1]. Unlike classic compression problems, the focus is not on reconstructing the original data. Instead, the compression rate is determined by the desired reliability of the answers. Specifically, the information measure identification rate of a compression scheme characterizes the minimum compression rate that can be achieved which guarantees reliable answers with respect to a given similarity threshold. In this paper, we study the component-based quadratic similarity identification for correlated sources. The blocks are first decorrelated by Karhunen-Loève transform. Then, the decorrelated data is processed by a distinct D-admissible system for each component. We derive the identification rate of component-based scheme for block-correlated Gaussian sources. In addition, we characterize the identification rate of a special setting where any information regarding to the component similarity thresholds is unknown while only the similarity threshold of the whole scheme is given. Furthermore, we prove that block-correlated Gaussian sources are the “most difficult” to code under the special setting.