Private Information Retrieval Through Wiretap Channel Ii

We consider the problem of private information retrieval through a wiretap channel II (PIR-WTC-II). In PIR-WTC-II, a user wants to retrieve a message (or file) privately out of M messages, which are stored in N replicated and non-communicating databases. An eavesdropper observes a fraction mu(n) of the traffic exchanged between the nth database and the user. The databases should encode the returned answer strings such that the eavesdropper learns nothing about the contents of the databases. We aim at characterizing the capacity of the PIR-WTC-II under these joint privacy and security constraints. We obtain an upper bound in the form of a max-min optimization problem. We propose an achievability scheme that satisfies the security constraint by encoding a secret key into an artificial noise vector using an MDS code. The user and the databases operate at one of the corner points of the achievable scheme of the PIR under asymmetric traffic constraints such that the retrieval rate is maximized under the imposed security constraint. The upper bound and the lower bound match for the cases of M = 2 and M = 3 messages, for any number of databases N, and any mu(n).