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Private Information Retrieval with Side Information
IEEE Transactions on Information Theory ( IF 2.5 ) Pub Date : 2020-04-01 , DOI: 10.1109/tit.2019.2948845
Swanand Kadhe , Brenden Garcia , Anoosheh Heidarzadeh , Salim El Rouayheb , Alex Sprintson

We study the problem of Private Information Retrieval (PIR) in the presence of prior side information. The problem setup includes a database of $K$ independent messages possibly replicated on several servers, and a user that needs to retrieve one of these messages. In addition, the user has some prior side information in the form of a subset of $M$ messages, not containing the desired message and unknown to the servers. This problem is motivated by practical settings in which the user can obtain side information opportunistically from other users or has previously downloaded some messages using classical PIR schemes. The objective of the user is to retrieve the required message with downloading minimum amount of data from the servers while achieving information-theoretic privacy in one of the following two scenarios: (i) the user wants to protect jointly the identities of the demand and the side information; (ii) the user wants to protect only the identity of the demand, but not necessarily the side information. To highlight the role of side information, we focus first on the case of a single server (single database). In the first scenario, we prove that the minimum download cost is $K-M$ messages, and in the second scenario it is $\lceil K/(M+1)\rceil $ messages, which should be compared to $K$ messages—the minimum download cost in the case of no side information. Then, we extend some of our results to the case of the database replicated on multiple servers. Our proof techniques relate PIR with side information to the index coding problem. We leverage this connection to prove converse results, as well as to design achievability schemes.

中文翻译:

带有辅助信息的私人信息检索

我们在存在先验辅助信息的情况下研究私人信息检索 (PIR) 问题。问题设置包括一个数据库 $K$ 可能在多个服务器上复制的独立消息,以及需要检索这些消息之一的用户。此外,用户有一些以子集形式的先验边信息 百万美元 消息,不包含所需的消息并且服务器未知。这个问题是由实际设置引起的,在这些设置中,用户可以从其他用户那里机会性地获取辅助信息,或者之前已经使用经典的 PIR 方案下载了一些消息。用户的目标是通过从服务器下载最少量的数据来检索所需的消息,同时在以下两种情况之一中实现信息论隐私:(i) 用户希望共同保护需求的身份和辅助资料;(ii) 用户只想保护需求的身份,而不必保护边信息。为了突出边信息的作用,我们首先关注单服务器(单数据库)的情况。在第一个场景中,我们证明最小下载成本是 $KM$ 消息,在第二种情况下是 $\lceil K/(M+1)\rceil $ 消息,应该比较 $K$ 消息——在没有辅助信息的情况下的最低下载成本。然后,我们将一些结果扩展到在多台服务器上复制数据库的情况。我们的证明技术将带有辅助信息的 PIR 与索引编码问题联系起来。我们利用这种联系来证明相反的结果,以及设计可实现性方案。
更新日期:2020-04-01
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