Cache-Aided Multi-User Private Information Retrieval Using PDAs

We consider the problem of cache-aided multi-user private information retrieval (MuPIR). This problem consists of
$N$
independent files that are replicated across
$S \geq 2$
non-colluding servers. There are
$K$
cache-equipped users having caches of size equivalent to
$M$
files. Every user aims to retrieve a file from the servers, but servers should not obtain any information about users’ demands. The user caches are filled with some arbitrary function of the files before the users decide their demands, known as the placement phase. After deciding their demands, users cooperatively send queries to the servers to retrieve their desired files privately. Upon receiving the queries, servers broadcast coded transmissions based on these queries and the files, known as the delivery phase. Conveying queries to the servers incurs an upload cost for the users, and downloading the answers broadcasted by the servers incurs a download cost. Each file has to be split into
$F$
packets to implement cache-aided MuPIR schemes. In this paper, we propose 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. The proposed scheme also substantially reduces the upload cost for the users. We show that our scheme is order optimal in terms of download cost for PDAs based on Ali-Niesen scheme for centralised coded caching. 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,” IEEE Trans. Inform. Theory, 2019] as a special case. Our scheme also achieves optimal rate for single-user cache-aided PIR setup reported in [R. Tandon, “The capacity of cache aided private information retrieval,” Annual Allerton Conference on Communication, Control and Computing, 2017.]