Private Information Retrieval from Non-Replicated Databases

We consider the problem of private information retrieval (PIR) of a single message out of K messages from N non-colluding and non-replicated databases. Different from the majority of the existing literature, here, we consider the case of non-replicated databases under a special non-replication structure where each database stores M out of K messages and each message is stored across R different databases. This generates an R-regular graph structure for the storage system where the vertices of the graph are the messages and the edges are the databases. We derive a general upper bound for M = 2 that depends on the graph structure. We then specialize the problem to storage systems described by two special types of graph structures: cyclic graphs and fully-connected graphs. We prove that the PIR capacity for the case of cyclic graphs is 2/K+1, and the PIR capacity for the case of fully-connected graphs is min{2/K, 1/2}. In both cases, the results show severe degradation in PIR capacity due to non-replication.