We propose capacity-achieving schemes for private information retrieval (PIR) from uncoded databases (DBs) with both homogeneous and heterogeneous storage constraints. In the PIR setting, a user queries a set of DBs to privately download a message, where privacy implies that no one DB can infer which message the user desires. In general, a PIR scheme is comprised of storage placement and delivery designs. Previous works have derived the capacity, or infimum download cost, of PIR with uncoded storage placement and sufficient conditions of storage placement to meet capacity. However, the currently proposed storage placement designs require splitting each message into an exponential number of sub-messages with respect to the number of DBs. In this work, when DBs have the same storage constraint, we propose two simple storage placement designs that satisfy the capacity conditions. Then, for more general heterogeneous storage constraints, we translate the storage placement design process into a “filling problem”. We design an iterative algorithm to solve the filling problem where, in each iteration, messages are partitioned into sub-messages and stored at subsets of DBs. All of our proposed storage placement designs require a number of sub-messages per message at most equal to the number of DBs.

中文翻译：

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用于从存储受限数据库中检索私人信息的带有线性子消息的未编码放置

我们为来自未编码数据库 (DB) 的私有信息检索 (PIR) 提出了容量实现方案，同时具有同构和异构存储约束。在 PIR 设置中，用户查询一组 DB 以私下下载消息，其中隐私意味着没有一个 DB 可以推断出用户想要的消息。通常，PIR 方案由存储放置和交付设计组成。以前的工作已经推导出具有未编码存储位置和足够的存储位置条件以满足容量的 PIR 的容量或最小下载成本。然而，当前提出的存储放置设计需要将每条消息拆分为与 DB 数量相关的指数数量的子消息。在这项工作中，当 DB 具有相同的存储约束时，我们提出了两种满足容量条件的简单存储放置设计。然后，对于更一般的异构存储约束，我们将存储布局设计过程转化为“填充问题”。我们设计了一种迭代算法来解决填充问题，其中在每次迭代中，消息被划分为子消息并存储在 DB 的子集中。我们提出的所有存储布局设计都要求每个消息的子消息数量最多等于 DB 的数量。