Multiround Private Information Retrieval: Capacity and Storage Overhead

Private information retrieval (PIR) is the problem of retrieving one message out of K messages from N noncommunicating replicated databases, where each database stores all K messages, in such a way that each database learns no information about which message is being retrieved. The capacity of PIR is the maximum number of bits of desired information per bit of downloaded information among all PIR schemes. The capacity has recently been characterized for PIR as well as several of its variants. In every case it is assumed that all the queries are generated by the user simultaneously. Here we consider multiround PIR, where the queries in each round are allowed to depend on the answers received in previous rounds. We show that the capacity of multiround PIR is the same as the capacity of single-round PIR. The result is generalized to also include T-privacy constraints. Combined with previous results, this shows that there is no capacity advantage from multiround over single-round schemes, non-linear over linear schemes or from E-error over zero-error schemes. However, we show through an example that there is an advantage in terms of storage overhead. We provide an example of a multiround, non-linear, E-error PIR scheme that requires a strictly smaller storage overhead than the best possible with single-round, linear, zero-error PIR schemes.