Private Information Retrieval in Distributed Storage Systems Using an Arbitrary Linear Code

TL;DR

This paper introduces a new private information retrieval scheme for distributed storage that leverages linear codes to enhance privacy and reduce communication costs, generalizing previous MDS code-based methods.

Contribution

It extends PIR schemes to arbitrary linear systematic codes with rate > 1/2 and provides an algorithm to optimize communication efficiency based on code structure.

Findings

The scheme generalizes previous PIR methods for MDS codes.

The optimization algorithm significantly reduces communication costs.

Application to various codes demonstrates improved privacy efficiency.

Abstract

We propose an information-theoretic private information retrieval (PIR) scheme for distributed storage systems where data is stored using a linear systematic code of rate $R > 1/2$. The proposed scheme generalizes the PIR scheme for data stored using maximum distance separable codes recently proposed by Tajeddine and El Rouayheb for the scenario of a single spy node. We further propose an algorithm to optimize the communication price of privacy (cPoP) using the structure of the underlying linear code. As an example, we apply the proposed algorithm to several distributed storage codes, showing that the cPoP can be significantly reduced by exploiting the structure of the distributed storage code.