Multi-Access Cache-Aided Multi-User Private Information Retrieval

We consider the problem of multi-access cache-aided multi-user Private Information Retrieval (MuPIR). In this problem, several files are replicated across multiple servers. There are $K$ users and $C$ cache nodes. Each user can access $L$ cache nodes, and every cache node can be accessed by several users. Each user wants to retrieve one file from the servers, but the users do not want the servers to know their demands. Before the users decide their respective demands, servers will fill the cache nodes from the content of the files. Users will then request their desired files from the servers. Servers will perform coded transmissions, and all the users should get their desired files from these transmissions and the content placed in the caches they are accessing. It is required that any individual server should not get any information about the demands of the users. This problem is an extension of the dedicated cache-aided MuPIR problem, which itself generalizes the widely studied single user PIR setup. In this paper, we propose a MuPIR scheme which utilizes a multi-access setup of the coded caching problem. The presented scheme is order optimal when $K=\binom{C}{L}$ users. We also characterize the rate of the scheme for the special case of cyclic wraparound multi-access setup, where $C=K$ and each user access $L$ consecutive cache nodes in cyclic wraparound fashion.