Fundamental limits for information retrieval

The fundamental limits of performance for a general model of information retrieval from databases are studied. In the scenarios considered, a large quantity of information is to be stored on some physical storage device. Requests for information are modeled as a randomly generated sequence with a known distribution. The requests are assumed to be "context-dependent," i.e., to vary according to the sequence of previous requests. The state of the physical storage device is also assumed to depend on the history of previous requests. In general, the logical structure of the information to be stored does not match the physical structure of the storage device, and consequently there are nontrivial limits on the minimum achievable average access times, where the average is over the possible sequences of user requests. The paper applies basic information-theoretic methods to establish these limits and demonstrates constructive procedures that approach them, for a wide class of systems. Allowing redundancy greatly lowers the achievable access times, even when the amount added is an arbitrarily small fraction of the total amount of information in the database. The achievable limits both with and without redundancy are computed; in the case where redundancy is allowed the limits essentially coincide with lower limits for more general storage systems.