Cache-Aided Multi-User Private Information Retrieval using PDAs

We consider the problem of cache-aided multi-user private information retrieval (MuPIR). In this problem, each of K cache-equipped users wants to privately retrieve a file out of N files replicated across B non-colluding servers. The user caches are filled with some arbitrary function of the files before the users decide their demands, known as the placement phase. Then in the delivery phase, users decide their demands and send queries to the servers to retrieve their desired files. This paper proposes MuPIR schemes that utilize placement delivery arrays (PDAs) to characterize placement and delivery. Proposed MuPIR schemes significantly reduce subpacketization levels while slightly increasing the download cost for the users. The proposed scheme also substantially reduces the upload cost for the users. For PDAs based on Ali-Niesen scheme for centralized coded caching, we show that our scheme is order optimal in terms of download cost. We recover the optimal single-user PIR scheme presented by Tian et al. in "Capacity-Achieving Private Information Retrieval Codes With Optimal Message Size and Upload Cost" as a special case. Our scheme also achieves optimal rate for single-user cache-aided PIR setup as described by R. Tondon in "The capacity of cache aided private information retrieval".