Private Information Retrieval for Coded Storage

TL;DR

This paper investigates private information retrieval in coded data storage systems, analyzing the tradeoff between storage and retrieval costs, and proposing general linear schemes with conditions for privacy and error-freeness, especially for MDS codes.

Contribution

It introduces a general class of linear storage and retrieval schemes, deriving conditions for privacy and error-freeness, and analyzes the tradeoff between storage and retrieval costs.

Findings

Tradeoff between storage and retrieval costs depends on data record count.

Proposed linear schemes can be error-free and private under certain conditions.

Random retrieval schemes are likely to be private and error-free for MDS codes.

Abstract

Private information retrieval scheme for coded data storage is considered in this paper. We focus on the case where the size of each data record is large and hence only the download cost (but not the upload cost for transmitting retrieval queries) is of interest. We prove that the tradeoff between storage cost and retrieval/download cost depends on the number of data records in the system. We also propose a fairly general class of linear storage codes and retrieval schemes and derive conditions under which our retrieval schemes are error-free and private. Tradeoffs between the storage cost and retrieval costs are also obtained. Finally, we consider special cases when the underlying storage code is based on an MDS code. Using our proposed method, we show that a randomly generated retrieval scheme is indeed very likely to be private and error-free.