论文标题
单人服务私人信息检索与任意流行度下的附带信息一起检索
Single-Server Private Information Retrieval with Side Information Under Arbitrary Popularity Profiles
论文作者
论文摘要
本文介绍了私人信息检索的概括，并带有侧面信息（PIR-SI）问题，称为PURIANTIS-PIR-SI（PA-PIR-SI）。 PA-PIR-SI问题包括一个或多个存储$ K $消息数据集的副本的远程服务器，以及一个了解$ K $消息中$ M $的用户（服务器的身份是未知的）作为先前的信息，并希望检索其余的$ k-m $。用户的目的是最大程度地减少他们必须从服务器下载的信息量，同时透露有关所需消息的身份的信息。与PIR-SI相反，在PA-PIR-SI中，数据集消息不同样流行。也就是说，鉴于$ M $ side信息消息，其余的$ K-M $消息不一定是用户所需的消息。在这项工作中，我们专注于PA-PIR-SI的单人服务器设置，并根据此设置的能力建立下层和上限 - 定义为最大可能可实现的下载率。我们的上限符合任何消息流行度概况，并且与单人服务器PIR-SI的容量相同。我们通过提出PA-PIR-SI方案来证明下限，该方案采用一种新颖的概率方法（基于流行性概况仔细设计）来整合两个现有的PIR-SI方案。我们计划的速率严格高于适用于PA-PIR-SI设置的唯一现有的PIR-SI方案。
This paper introduces a generalization of the Private Information Retrieval with Side Information (PIR-SI) problem called Popularity-Aware PIR-SI (PA-PIR-SI). The PA-PIR-SI problem includes one or more remote servers storing copies of a dataset of $K$ messages, and a user who knows $M$ out of $K$ messages -- the identities of which are unknown to the server -- as a prior side information, and wishes to retrieve one of the remaining $K-M$ messages. The goal of the user is to minimize the amount of information they must download from the server while revealing no information about the identity of the desired message. In contrast to PIR-SI, in PA-PIR-SI, the dataset messages are not assumed to be equally popular. That is, given the $M$ side information messages, each of the remaining $K-M$ messages is not necessarily equally likely to be the message desired by the user. In this work, we focus on the single-server setting of PA-PIR-SI, and establish lower and upper bounds on the capacity of this setting -- defined as the maximum possible achievable download rate. Our upper bound holds for any message popularity profile, and is the same as the capacity of single-server PIR-SI. We prove the lower bound by presenting a PA-PIR-SI scheme which takes a novel probabilistic approach -- carefully designed based on the popularity profile -- to integrate two existing PIR-SI schemes. The rate of our scheme is strictly higher than that of the only existing PIR-SI scheme applicable to the PA-PIR-SI setting.
