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, $N$ independent files are replicated across $S \geq 2$ non-colluding servers. There are $K$ users, each equipped with cache memory which can store $M$ files. Each user wants to retrieve a file from the servers, but the users don't want any of the servers to get any information about their demand. 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 which are a function of the queries they received 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. To implement cache-aided MuPIR schemes, each file has to be split into $F$ packets. 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. For PDAs based on {\it 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 {\it Tian et al.} as a special case. Our scheme also achieves optimal rate for single-user cache-aided PIR setup reported by R. Tondon.Comment: 30 pages, 7 figures and 5 table

Hierarchical Cache-Aided Linear Function Retrieval with Security and Privacy Constraints

The hierarchical caching system where a server connects with multiple mirror sites, each connecting with a distinct set of users, and both the mirror sites and users are equipped with caching memories has been widely studied. However all the existing works focus on single file retrieval, i.e., each user requests one file, and ignore the security and privacy threats in communications. In this paper we investigate the linear function retrieval problem for hierarchical caching systems with content security and demand privacy, i.e., each user requests a linear combination of files, and meanwhile the files in the library are protected against wiretappers and users' demands are kept unknown to other users and unconnected mirror sites. First we propose a new combination structure named hierarchical placement delivery array (HPDA), which characterizes the data placement and delivery strategy of a coded caching scheme. Then we construct two classes of HPDAs. Consequently two classes of schemes with or without security and privacy are obtained respectively where the first dedicates to minimizing the transmission load for the first hop and can achieve the optimal transmission load for the first hop if ignoring the security and privacy constraints; the second has more flexible parameters on the memory sizes and a lower subpacketization compared with the first one, and achieves a tradeoff between subpacketization and transmission loads.Comment: arXiv admin note: substantial text overlap with arXiv:2205.0023

Demand-Private Coded Caching and the Exact Trade-off for N=K=2

The distributed coded caching problem has been studied extensively in the recent past. While the known coded caching schemes achieve an improved transmission rate, they violate the privacy of the users since in these schemes the demand of one user is revealed to others in the delivery phase. In this paper, we consider the coded caching problem under the constraint that the demands of the other users remain information theoretically secret from each user. We first show that the memory-rate pair $(M,\min \{N,K\}(1-M/N))$ is achievable under information theoretic demand privacy, while using broadcast transmissions. We then show that a demand-private scheme for $N$ files and $K$ users can be obtained from a non-private scheme that satisfies only a restricted subset of demands of $NK$ users for $N$ files. We then focus on the demand-private coded caching problem for $K=2$ users, $N=2$ files. We characterize the exact memory-rate trade-off for this case. To show the achievability, we use our first result to construct a demand-private scheme from a non-private scheme satisfying a restricted demand subset that is known from an earlier work by Tian. Further, by giving a converse based on the extra requirement of privacy, we show that the obtained achievable region is the exact memory-rate trade-off.Comment: 8 pages, 2 figure

On Cache-Aided Multi-User Private Information Retrieval with Small Caches

In this paper, we propose a scheme for the problem of cache-aided multi-user private information retrieval with small caches, in which $K$ users are connected to $S$ non-colluding databases via shared links. Each database contains a set of $N$ files, and each user has a dedicated cache of size equivalent to the size of $M$ files. All the users want to retrieve a file without revealing their demands to the databases. During off-peak hours, all the users will fill their caches, and when required, users will demand their desired files by cooperatively generating query sets for each database. After receiving the transmissions from databases, all the users should get their desired files using transmitted data and their cache contents. This problem has been studied in [X. Zhang, K. Wan, H. Sun, M. Ji and G. Caire, \tqt{Fundamental limits of cache-aided multiuser private information retrieval}, IEEE Trans. Commun., 2021], in which authors proposed a product design scheme. In this paper, we propose a scheme that gives a better rate for a particular value of $M$ than the product design scheme. We consider a slightly different approach for the placement phase. Instead of a database filling the caches of all users directly, a database will broadcast cache content for all users on a shared link, and then the users will decide unitedly which part of the broadcasted content will be stored in the cache of each user. This variation facilitates maintaining the privacy constraint at a reduced rate.Comment: 32 pages, 7 tables and 1 figur