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arXiv · 1903.06921

A new Capacity-Achieving Private Information Retrieval Scheme with (Almost) Optimal File Length for Coded Servers

Jinbao Zhu·Qifa Yan·Chao Qi·Xiaohu Tang
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Abstract

In a distributed storage system, private information retrieval (PIR) guarantees that a user retrieves one file from the system without revealing any information about the identity of its interested file to any individual server. In this paper, we investigate $(N,K,M)$ coded sever model of PIR, where each of $M$ files is distributed to the $N$ servers in the form of $(N,K)$ maximum distance separable (MDS) code for some $N>K$ and $M>1$. As a result, we propose a new capacity-achieving $(N,K,M)$ coded linear PIR scheme such that it can be implemented with file length $\frac{K(N-K)}{\gcd(N,K)}$, which is much smaller than the previous best result $K\big(\frac{N}{\gcd(N,K)}\big)^{M-1}$. Notably, among all the capacity-achieving coded linear PIR schemes, we show that the file length is optimal if $M>\big\lfloor \frac{K}{\gcd(N,K)}-\frac{K}{N-K}\big\rfloor+1$, and within a multiplicative gap $\frac{K}{\gcd(N,K)}$ of a lower bound on the minimum file length otherwise.

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Jinbao Zhu, Qifa Yan, Chao Qi, Xiaohu Tang. 2019-03-16. A new Capacity-Achieving Private Information Retrieval Scheme with (Almost) Optimal File Length for Coded Servers. https://arxiv.org/abs/1903.06921

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