Single-Server Individually-Private Information Retrieval: A Combinatorial Approach

This paper considers the problem of single-server Individually-Private Information Retrieval (IPIR). In this problem, a user wants to retrieve \(D\) messages belonging to a dataset of \(K\) messages stored on a single server. Initially, the user knows \(M\) other messages belonging to the dataset as side information, where the identities of these \(M\) messages are unknown to the server. The goal is to minimize the total amount of information that the user must download from the server while keeping the identity of each of the \(D\) desired messages individually private, i.e., the identity of every individual message wanted by the user must be protected. The capacity of IPIR, which is defined as the supremum of all achievable download rates, was previously characterized for \(D=2, M=1\). However, the capacity was left open for all other values of \(D, M\). In this work, we present a technique for the proof of converse, based on a novel combinatorial approach. Using this technique, we establish an upper bound on the capacity of IPIR for \(D=2, M=2\). For this setting, we also propose a new IPIR scheme---based on a probabilistic partitioning of the messages, that achieves the capacity upper bound. We believe that our approach can be employed for proving the converse and designing optimal schemes for the general cases of the problem.