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.]

In a Multi-user Private Information Retrieval (MuPIR) problem, there areNfiles replicated acrossSnon-colluding servers andKusers, each wanting to retrieve a file from the servers without letting the servers getting any information about the demanded files. In a dedicated-cache-aided MuPIR problem each user is equipped with a cache that can storeMfiles. In this paper, we consider a generalized version, called multi-access cache-aided MuPIR problem, where there areKusers andC≤Kcaches each capable of storingMfiles and each user can access several cache nodes and every cache node can be accessed by several users. The cache nodes are filled with the content of the files before users decide their demands. Then each user chooses a file index, and users cooperatively send queries to the servers to retrieve their desired files privately. The aim is to reduce the size of broadcast done by the servers as a response to these queries. We propose a scheme that utilizes multi-access caches in generalised combinatorial topology, introduced by Brunero and Elia in [13] and show that our scheme is order-optimal within a multiplicative factor of 2, assuming uncoded cache placement. Also, we compare the per-user rate of our setup with dedicated cache setup of [10] in various settings.

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".

In private information delivery (PID) problem, there are K messages stored across N servers, each capable of storing M messages and a user. Servers want to convey one of the K messages to the user without revealing the identity (index) of the message conveyed. The capacity of PID problem is defined as the maximum number of bits of the desired message that can be conveyed privately, per bit of total communication, to the user. For the restricted case of replicated systems, where coded messages or splitting one message into several servers is not allowed, the capacity of PID has been characterized by Hua Sun in "Private Information Delivery, IEEE Transactions on Information Theory, December 2020" in terms of K, N and M. In this paper, we study the problem of PID with coded storage at the servers. For a class of problems called bi-regular PID we characterize the capacity for N = K/M and for N > K/M we provide achievable scheme. In both the cases, the rates achieved are more than the rates achievable with the replicated systems.

In this paper, we consider the multi-access cache-aided multi-user Private Information Retrieval (MuPIR) problem. In this problem, N files are replicated across S servers. There are K users and C cache nodes, each capable of storing M files. 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 users don’t want the servers to know their demands. This problem is an extension of the dedicated cache-aided MuPIR problem, which itself generalizes the single-user PIR setup. In this paper, we propose an order optimal MuPIR scheme that utilizes a multi-access setup of the coded caching problem where every set of L caches is accessed by one user resulting in K=$\begin{pmatrix} c\\ L \end{pmatrix}$. We also propose

In a distributed computation system, there is a master node who wants to compute a function of its own data by distributing the computation amongst several worker nodes. In distributed computation system considered here, the master wants to multiply two matrices, one owned by the master and other matrix is in the library of matrices shared by the worker nodes. The master divides the computation task among these nodes. After recovering the desired computation, any set of up to T colluding workers should not know which matrix in the library was desired by the master, referred to as demand privacy and also do not have any information about master's matrix, referred to as data privacy. In this paper, a distributed computing scheme is proposed that simultaneously ensures (1) data and demand privacy of the master against colluding workers (2) straggler mitigation and (3) security against malicious workers. Similar matrix multiplication scenario was considered against non-colluding worker nodes by M. Kim and J. Lee in Private Secure Coded Computation.