The Capacity of Private Information Retrieval with Private Side Information

The problem of private information retrieval with private side information (PIR-PSI) is recently introduced by Kadhe et al. In this problem, N replicated databases each store K messages, of which M are known to the user as side-information. The identity of these M messages is unknown to the databases. The user wishes to retrieve, as efficiently as possible, a new desired message without revealing any information about the joint indices of the desired and sideinformation messages. We show that the capacity of PIR-PSI is ( 1 + 1 N + 1 N + · · ·+ 1 N ) −1 . Thus, the capacity of PIR-PSI with K messages, N databases and side-information of M messages is identical to the capacity of PIR with K − M messages, N databases and no sideinformation, which was found previously by Sun and Jafar. The achievability and converse proofs are essentially inherited from the original work of Sun and Jafar.