Optimal Rate-Distortion-Leakage Tradeoff for Single-Server Information Retrieval

TL;DR

This paper explores the balance between download rate, data distortion, and information leakage in single-server private information retrieval, proposing optimal tradeoffs and new construction methods for finite file sizes.

Contribution

It derives the optimal rate-distortion-leakage tradeoff for infinite files and introduces a linear programming approach for finite files, including explicit solutions for small database sizes.

Findings

Optimal tradeoff formulas for infinite file size.

Closed-form solutions for no-leakage and no-privacy cases.

LP-based schemes for finite file sizes up to four bits.

Abstract

Private information retrieval protocols guarantee that a user can privately and losslessly retrieve a single file from a database stored across multiple servers. In this work, we propose to simultaneously relax the conditions of perfect retrievability and privacy in order to obtain improved download rates when all files are stored uncoded on a single server. Information leakage is measured in terms of the average success probability for the server of correctly guessing the identity of the desired file. The main findings are: i) The derivation of the optimal tradeoff between download rate, distortion, and information leakage when the file size is infinite. Closed-form expressions of the optimal tradeoff for the special cases of "no-leakage" and "no-privacy" are also given. ii) A novel approach based on linear programming (LP) to construct schemes for a finite file size and an arbitrary number of files. The proposed LP approach can be leveraged to find provably optimal schemes with corresponding closed-form expressions for the rate-distortion-leakage tradeoff when the database contains at most four bits. Finally, for a database that contains 320 bits, we compare two construction methods based on the LP approach with a nonconstructive scheme downloading subsets of files using a finite-length lossy compressor based on random coding.