The Capacity of Semantic Private Information Retrieval with Colluding Servers

TL;DR

This paper determines the exact capacity of semantic private information retrieval with colluding servers, generalizing classical PIR to account for variable message sizes, non-uniform retrieval probabilities, and server collusions.

Contribution

It derives the exact capacity of Sem-TPIR for arbitrary collusion levels and designs a scheme achieving this capacity, extending prior work to more general settings.

Findings

Established an upper bound on retrieval rate.

Designed a scheme that achieves the capacity.

Generalized PIR to variable message sizes and non-uniform retrieval probabilities.

Abstract

We study the problem of semantic private information retrieval (Sem-PIR) with $T$ colluding servers (Sem-TPIR), i.e., servers that collectively share user queries. In Sem-TPIR, the message sizes are different, and message retrieval probabilities by any user are not uniform. This is a generalization of the classical PIR problem where the message sizes are equal and message retrieval probabilities are identical. The earlier work on Sem-PIR considered the case of no collusions, i.e., the collusion parameter of $T=1$. In this paper, we consider the general problem for arbitrary $T < N$. We find an upper bound on the retrieval rate and design a scheme that achieves this rate, i.e., we derive the exact capacity of Sem-TPIR.