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Private Information Retrieval from Non-Replicated Databases with Optimal Message Size

In this paper, we consider the private information retrieval problem over a storage system where the files are not replicated at all databases. This kind of storage system represents a non-replicated database structure and was first introduced by Banawan-Ulukus. Specifically, we assume that M out of K messages are stored across R databases. When R=M=2, the storage system can be modeled by a cyclic graph structure. For this case, we show that the message length of one bit is sufficient to achieve the capacity. Our achievable scheme uses the method of Tian-Sun-Chen where an asymmetric structure for answers from databases is proposed. A main characteristic of our proposed scheme is the fact that the query structure does not depend on the number of databases implying the scalability of the scheme. Finally, we discuss an example where our proposed scheme can achieve a larger retrieval rate than the one derived by Banawan-Ulukus.