Degeneracy bounds for private information retrieval protocols

Protocols to retrieve information which hide the query allows a user to get the desired information bit from a database replicated on several noncommunicating servers in such a way that the administrator of the database knows nothing about the index of the bit the user queries. A protocol is said to be degenerate if the user, as the result of the query, gets the whole database. We find bounds for protocol parameters where the degeneracy can be obviated.