A Shannon-Theoretic Approach to the Storage-Retrieval Tradeoff in PIR Systems

TL;DR

This paper introduces a Shannon-theoretic approach to analyze the storage-retrieval tradeoff in PIR systems, proposing a novel non-linear coding scheme that outperforms linear schemes and establishing bounds for optimal performance.

Contribution

It presents a new non-linear coding scheme for PIR, revealing a connection to multiple description coding and demonstrating improved tradeoffs over linear methods.

Findings

Non-linear schemes outperform linear schemes at optimal retrieval rates.

A new storage-retrieval tradeoff beyond space-sharing is achievable.

Outer bounds show the superiority of non-linear codes over linear codes.

Abstract

We consider the storage-retrieval rate tradeoff in private information retrieval (PIR) systems using a Shannon-theoretic approach. Our focus is mostly on the canonical two-message two-database case, for which a coding scheme based on random codebook generation and the binning technique is proposed. This coding scheme reveals a hidden connection between PIR and the classic multiple description source coding problem. We first show that when the retrieval rate is kept optimal, the proposed non-linear scheme can achieve better performance over any linear scheme. Moreover, a non-trivial storage-retrieval rate tradeoff can be achieved beyond space-sharing between this extreme point and the other optimal extreme point, achieved by the retrieve-everything strategy. We further show that with a method akin to the expurgation technique, one can extract a zero-error PIR code from the random code. Outer bounds are also studied and compared to establish the superiority of the non-linear codes over linear codes.