The Linear Capacity of Single-Server Individually-Private Information Retrieval with Side Information

TL;DR

This paper characterizes the maximum download rate for linear single-server individually-private information retrieval with side information, establishing a capacity bound and its achievability under certain conditions.

Contribution

It provides the first complete characterization of the linear capacity of IPIR with side information, including a tight converse bound and achievable schemes for many parameters.

Findings

Converse bound on the download rate for all parameters.

Achievability of the bound under a divisibility condition.

Complete characterization of linear capacity for a wide range of parameters.

Abstract

This paper considers the problem of single-server Individually-Private Information Retrieval with side information (IPIR). In this problem, there is a remote server that stores a dataset of $K$ messages, and there is a user that initially knows $M$ of these messages, and wants to retrieve $D$ other messages belonging to the dataset. The goal of the user is to retrieve the $D$ desired messages by downloading the minimum amount of information from the server while revealing no information about whether an individual message is one of the $D$ desired messages. In this work, we focus on linear IPIR schemes, i.e., the IPIR schemes in which the user downloads only linear combinations of the original messages from the server. We prove a converse bound on the download rate of any linear IPIR scheme for all $K,D,M$, and show the achievability of this bound for all $K,D,M$ satisfying a certain divisibility condition. Our results characterize the linear capacity of IPIR, which is defined as the maximum achievable download rate over all linear IPIR schemes, for a wide range of values of $K,D,M$.