A New Approach to Harnessing Side Information in Multi-Server Private Information Retrieval
Ningze Wang, Anoosheh Heidarzadeh, Alex Sprintson
TL;DR
The paper tackles Private Information Retrieval with Side Information (PIR-SI) in a multi-server setting, introducing a randomized, non-symmetric retrieval scheme that leverages side information while keeping the demand index private. It derives a capacity lower bound $R = (N-1)\left(N- \left(1+\sum_{k=1}^{g-1} r_k (N-1)^k \right)^{-1}\right)^{-1}$ with $g=\lceil K/(M+1)\rceil$ and $r_k=\prod_{j=1}^k \frac{K/(M+1)-j}{j}$, and shows $R^*= rac{N^{g}-N^{g-1}}{N^{g}-1}$ is a benchmark; the scheme achieves $R$ with linear sub-packetization $L=N-1$ and may surpass $R^*$ when $K$ is not divisible by $M+1$, even invalidating a previously claimed converse bound. The method relies on randomized construction of query linear combinations and non-uniform query distributions, exploiting the fact that the side information identity need not be private. An illustrative example demonstrates a concrete rate gain and verifies privacy and recoverability of the scheme. Overall, the work advances practical PIR-SI designs with lower sub-packetization while achieving higher download rates than prior approaches.
Abstract
This paper presents new solutions for Private Information Retrieval (PIR) with side information. This problem is motivated by PIR settings in which a client has side information about the data held by the servers and would like to leverage this information in order to improve the download rate. The problem of PIR with side information has been the subject of several recent studies that presented achievability schemes as well as converses for both multi-server and single-server settings. However, the solutions for the multi-server settings adapted from the solutions for the single-server setting in a rather straightforward manner, relying on the concept of super-messages. Such solutions require an exponential degree of sub-packetization (in terms of the number of messages). This paper makes the following contributions. First, we revisit the PIR problem with side information and present a new approach to leverage side information in the context of PIR. The key idea of our approach is a randomized algorithm to determine the linear combinations of the sub-packets that need to be recovered from each server. In addition, our approach takes advantage of the fact that the identity of the side information messages does not need to be kept private, and, as a result, the information retrieval scheme does not need to be symmetric. Second, we present schemes for PIR with side information that achieve a higher rate than previously proposed solutions and require a significantly lower degree of sub-packetization (linear in the number of servers). Our scheme not only achieves the highest known download rate for the problem at hand but also invalidates a previously claimed converse bound on the maximum achievable download rate.