On the Storage Cost of Private Information Retrieval

TL;DR

This paper explores the fundamental tradeoff between storage and download costs in private information retrieval systems, providing new bounds and insights into optimal strategies without structural restrictions on storage codes.

Contribution

It introduces two novel outer bounds on storage and download costs, and analyzes the two-message, two-database case with a new pseudo-message technique.

Findings

Optimal PIR with no redundancy involves downloading all messages.

For capacity-achieving codes, storage can be reduced by at most one message per database.

Stronger bounds suggest the need for non-Shannon inequalities for precise characterization.

Abstract

We consider the fundamental tradeoff between the storage cost and the download cost in private information retrieval systems, without any explicit structural restrictions on the storage codes, such as maximum distance separable codes or uncoded storage. Two novel outer bounds are provided, which have the following implications. When the messages are stored without any redundancy across the databases, the optimal PIR strategy is to download all the messages; on the other hand, for PIR capacity-achieving codes, each database can reduce the storage cost, from storing all the messages, by no more than one message on average. We then focus on the two-message two-database case, and show that a stronger outer bound can be derived through a novel pseudo-message technique. This stronger outer bound suggests that a precise characterization of the storage-download tradeoff may require non-Shannon type inequalities, or at least more sophisticated bounding techniques.