Identification Rate, Search and Memory Complexity Tradeoff: Fundamental Limits

In an information-theoretic framework, we introduce a two-stage decoding scheme capable of achieving identification capacity to address search and memory complexities in large-scale identification systems. This two-stage decoding procedure is accomplished as follows. For a given query, at the first stage, a list of cluster indices is estimated. Then, at the second stage, refinement checks are performed for all the members of the clusters to produce a single index. The first result this paper presents is the achievable rate quadruple region that specifies necessary conditions that the two-stage decoding scheme should satisfy to be able to achieve the identification capacity. The rest of this paper is designated to investigate various achievable rate quadruples in which the proposed two-stage identification setup can reduce the search complexity with respect to conventional identification setups.