Private Information Retrieval for a Multi-Message Scenario With Private Side Information

We consider the problem of private information retrieval (PIR), where a single user with private side information (PSI) aims to retrieve multiple files from a library stored at some servers. We assume that the side information (SI) at the user includes a subset of files stored privately. Moreover, the identity of requests and side information at the user are not revealed to any of the servers. The problem involves finding the minimum load transmitted from the servers to the user such that the requested files can be decoded with the help of received data and side information. By providing matching lower and upper bounds for certain regimes, we characterize the minimum load imposed on all the servers. Our result shows that the capacity is the same as the capacity of a multi-message PIR problem without PSI, but with a library of reduced size, i.e., the library is equal to the original library size minus the size of SI. Finally, we extend our setup to the case where instead of storing complete files as SI, the user can store a fraction of files. For this scenario, we propose an achievability scheme based on which we discuss the best storing strategies.