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# Cache-Aided Multi-User Private Information Retrieval using PDAs

Dec 2022

We consider the problem of cache-aided multi-user private informationretrieval (MuPIR). In this problem, $N$ independent files are replicated across$S \geq 2$ non-colluding servers. There are $K$ users, each equipped with cachememory which can store $M$ files. Each user wants to retrieve a file from theservers, but the users don't want any of the servers to get any informationabout their demand. The user caches are filled with some arbitrary function ofthe files before the users decide their demands, known as the placement phase.After deciding their demands, users cooperatively send queries to the serversto retrieve their desired files privately. Upon receiving the queries, serversbroadcast coded transmissions which are a function of the queries they receivedand the files, known as the delivery phase. Conveying queries to the serversincurs an upload cost for the users, and downloading the answers broadcasted bythe servers incurs a download cost. To implement cache-aided MuPIR schemes,each file has to be split into $F$ packets. In this paper, we propose MuPIRschemes that utilize placement delivery arrays (PDAs) to characterize placementand delivery. Proposed MuPIR schemes significantly reduce subpacketizationlevels while slightly increasing the download cost. The proposed scheme alsosubstantially reduces the upload cost for the users. For PDAs based on {\itAli-Niesen} scheme for centralized coded caching, we show that our scheme isorder optimal in terms of download cost. We recover the optimal single-user PIRscheme presented by {\it Tian et al.} as a special case. Our scheme alsoachieves optimal rate for single-user cache-aided PIR setup reported by R.Tondon.

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