Home
Scholarly Works
Capacity-Achieving Private Information Retrieval...
Journal article

Capacity-Achieving Private Information Retrieval Codes With Optimal Message Size and Upload Cost

Abstract

We propose a new capacity-achieving code for the private information retrieval (PIR) problem, and show that it has the minimum message size (being one less than the number of servers) and the minimum upload cost (being roughly linear in the number of messages) among a general class of capacity-achieving codes, and in particular, among all capacity-achieving linear codes. Different from existing code constructions, the proposed code is asymmetric, and this asymmetry appears to be the key factor leading to the optimal message size and the optimal upload cost. The converse results on the message size and the upload cost are obtained by an analysis of the information theoretic proof of the PIR capacity, from which a set of critical properties of any capacity-achieving code in the code class of interest is extracted. The symmetry structure of the PIR problem is then analyzed, which allows us to construct symmetric codes from asymmetric ones, yielding a meaningful bridge between the proposed code and existing ones in the literature.

Authors

Tian C; Sun H; Chen J

Journal

IEEE Transactions on Information Theory, Vol. 65, No. 11, pp. 7613–7627

Publisher

Institute of Electrical and Electronics Engineers (IEEE)

Publication Date

November 1, 2019

DOI

10.1109/tit.2019.2918207

ISSN

0018-9448

Contact the Experts team