# Single-Server Multi-Message Individually-Private Information Retrieval with Side Information

## TL;DR

This paper studies a multi-user private information retrieval system with side information, introducing individual privacy constraints and establishing capacity bounds with novel protocols and conjectures.

## Contribution

It introduces the IPIR-SI problem, derives a lower bound on capacity, characterizes capacity for specific parameters, and proposes a new combinatorial conjecture.

## Key findings

- Established a lower bound on the capacity of IPIR-SI.
- Characterized the capacity for M=1 and D=2.
- Proposed a novel combinatorial conjecture related to capacity.

## Abstract

We consider a multi-user variant of the private information retrieval problem described as follows. Suppose there are $D$ users, each of which wants to privately retrieve a distinct message from a server with the help of a trusted agent. We assume that the agent has a random subset of $M$ messages that is not known to the server. The goal of the agent is to collectively retrieve the users' requests from the server. For protecting the privacy of users, we introduce the notion of individual-privacy -- the agent is required to protect the privacy only for each individual user (but may leak some correlations among user requests). We refer to this problem as Individually-Private Information Retrieval with Side Information (IPIR-SI). We first establish a lower bound on the capacity, which is defined as the maximum achievable download rate, of the IPIR-SI problem by presenting a novel achievability protocol. Next, we characterize the capacity of IPIR-SI problem for $M = 1$ and $D = 2$. In the process of characterizing the capacity for arbitrary $M$ and $D$ we present a novel combinatorial conjecture, that may be of independent interest.