Capacity of Single-Server Single-Message Private Information Retrieval with Coded Side Information

TL;DR

This paper investigates the capacity of single-server private information retrieval with coded side information, providing upper bounds and optimal protocols for different scenarios to minimize download costs.

Contribution

It introduces new capacity bounds and optimal retrieval protocols for PIR with coded side information, considering different demand scenarios.

Findings

Derived upper bounds on download rate for both settings.

Proposed protocols achieve the derived capacity bounds.

Analyzed the impact of side information on retrieval efficiency.

Abstract

This paper considers the problem of single-server single-message private information retrieval with coded side information (PIR-CSI). In this problem, there is a server storing a database, and a user which knows a linear combination of a subset of messages in the database as a side information. The number of messages contributing to the side information is known to the server, but the indices and the coefficients of these messages are unknown to the server. The user wishes to download a message from the server privately, i.e., without revealing which message it is requesting, while minimizing the download cost. In this work, we consider two different settings for the PIR-CSI problem depending on the demanded message being or not being one of the messages contributing to the side information. For each setting, we prove an upper bound on the maximum download rate as a function of the size of the database and the size of the side information, and propose a protocol that achieves the rate upper-bound.