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Improved Storage for Efficient Private Information Retrieval

29 August 2019
Karim A. Banawan
Batuhan Arasli
S. Ulukus
ArXiv (abs)PDFHTML
Abstract

We consider the problem of private information retrieval from NNN \emph{storage-constrained} databases. In this problem, a user wishes to retrieve a single message out of MMM messages (of size LLL) without revealing any information about the identity of the message to individual databases. Each database stores μML\mu MLμML symbols, i.e., a μ\muμ fraction of the entire library, where 1N≤μ≤1\frac{1}{N} \leq \mu \leq 1N1​≤μ≤1. Our goal is to characterize the optimal tradeoff curve for the storage cost (captured by μ\muμ) and the normalized download cost (D/LD/LD/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.

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