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.

翻译：本文提出了在具有辅助信息的私密信息检索（PIR）问题中的新解决方案。该问题源于以下PIR场景：客户端拥有关于服务器所持有数据的辅助信息，并希望利用这些信息来提高下载速率。具有辅助信息的PIR问题已成为近期多项研究的主题，这些研究针对多服务器和单服务器场景分别提出了可实现性方案及逆界。然而，针对多服务器场景的解决方案往往是从单服务器场景的解决方案中直接改编而来，依赖于“超级消息”（super-messages）的概念，这类方案需要指数级的子包化程度（相对于消息数量而言）。本文做出以下贡献：首先，我们重新审视了具有辅助信息的PIR问题，并提出了一种在PIR背景下利用辅助信息的新方法。该方法的核心思想是通过一种随机化算法来确定需要从每个服务器恢复的子包的线性组合。此外，我们的方法利用了辅助信息消息的身份无需保密这一事实，从而使得信息检索方案无需保持对称性。其次，我们提出了具有辅助信息的PIR方案，该方案不仅实现了比先前方案更高的速率，而且显著降低了子包化程度（与服务器数量呈线性关系）。我们的方案不仅达到了当前已知的最高下载速率，而且还推翻了一个先前声称的最大可达下载速率逆界。