On the Fundamental Limits of Cache-aided Multiuser Private Information Retrieval

TL;DR

This paper explores the fundamental limits of cache-aided multiuser private information retrieval, proposing novel interference alignment and product design methods to optimize the trade-off between cache memory and communication load.

Contribution

It introduces cache-aided interference alignment and a product design approach, providing optimal or near-optimal solutions for multiuser PIR with caching.

Findings

CIA approach is optimal for 2-message, 2-user cases with uncoded cache placement.

Product design achieves order optimality within a factor of 8 for general parameters.

Optimality verified for small N (2 and 3) through computer-aided methods.

Abstract

We consider the problem of cache-aided Multiuser Private Information Retrieval (MuPIR) which is an extension of the single-user cache-aided PIR problem to the case of multiple users. In MuPIR, each of the $K_{\rm u}$ cache-equipped users wishes to privately retrieve a message out of $K$ messages from $N$ databases each having access to the entire message library. The privacy constraint requires that any individual database learns nothing about the demands of all users. The users are connected to each database via an error-free shared-link. In this paper, we aim to characterize the optimal trade-off between users' memory and communication load for such systems. Based on the proposed novel approach of \emph{cache-aided interference alignment (CIA)}, first, for the MuPIR problem with $K=2$ messages, $K_{\rm u}=2$ users and $N\ge 2$ databases, we propose achievable retrieval schemes for both uncoded and general cache placement. The CIA approach is optimal when the cache placement is uncoded. For general cache placement, the CIA approach is optimal when $N=2$ and $3$ verified by the computer-aided approach. Second, when $K,K_{\rm u}$ and $N$ are general, we propose a new \emph{product design} (PD) which incorporates the PIR code into the linear caching code. The product design is shown to be order optimal within a multiplicative factor of 8 and is exactly optimal when the user cache memory size is large.