Improved Storage for Efficient Private Information Retrieval

TL;DR

This paper introduces a hybrid storage scheme combining MDS coding and uncoded partial replication to optimize private information retrieval from storage-constrained databases, reducing download costs.

Contribution

It proposes a novel hybrid storage scheme that outperforms existing methods by balancing coding and replication for PIR.

Findings

Hybrid scheme reduces download cost compared to existing methods.

Scheme generalizes and improves upon previous storage schemes.

Optimal tradeoff curve between storage and download cost characterized.

Abstract

We consider the problem of private information retrieval from $N$ \emph{storage-constrained} databases. In this problem, a user wishes to retrieve a single message out of $M$ messages (of size $L$) without revealing any information about the identity of the message to individual databases. Each database stores $\mu ML$ symbols, i.e., a $\mu$ fraction of the entire library, where $\frac{1}{N} \leq \mu \leq 1$. Our goal is to characterize the optimal tradeoff curve for the storage cost (captured by $\mu$) and the normalized download cost ($D/L$). We show that the download cost can be reduced by employing a hybrid storage scheme that combines \emph{MDS coding} ideas with \emph{uncoded partial replication} ideas. When there is no coding, our scheme reduces to Attia-Kumar-Tandon storage scheme, which was initially introduced by Maddah-Ali-Niesen in the context of the caching problem, and when there is no uncoded partial replication, our scheme reduces to Banawan-Ulukus storage scheme; in general, our scheme outperforms both.