On the Fundamental Limit of Private Information Retrieval for Coded Distributed Storage

TL;DR

This paper investigates the maximum achievable private information retrieval rates in distributed storage systems using non-MDS linear codes, establishing the PIR capacity for a new class of codes and proposing improved asymmetric protocols.

Contribution

It proves the PIR capacity equals the MDS-PIR capacity for a new class of non-MDS codes and introduces asymmetric PIR protocols with higher rates for other codes.

Findings

PIR capacity is equal to MDS-PIR capacity for certain non-MDS codes.

Asymmetric PIR protocols outperform symmetric ones in some cases.

First characterization of PIR capacity for this class of non-MDS codes.

Abstract

We consider private information retrieval (PIR) for distributed storage systems (DSSs) with noncolluding nodes where data is stored using a non maximum distance separable (MDS) linear code. It was recently shown that if data is stored using a particular class of non-MDS linear codes, the MDS-PIR capacity, i.e., the maximum possible PIR rate for MDS-coded DSSs, can be achieved. For this class of codes, we prove that the PIR capacity is indeed equal to the MDS-PIR capacity, giving the first family of non-MDS codes for which the PIR capacity is known. For other codes, we provide asymmetric PIR protocols that achieve a strictly larger PIR rate compared to existing symmetric PIR protocols.