We consider the problem of cache-aided Multiuser Private Information Retrieval (MuPIR) which is an extension of the single-user cache-aided PIR problem to the case of multiple users. In cache-aided MuPIR, each of the $K_{\mathrm{ u}}$ cache-equipped users wishes to privately retrieve a message out of $K$ messages from $N$ databases each having access to the entire message library. Demand privacy requires that any individual database learns nothing about the demands of all users. The users are connected to each database via an error-free shared-link. In this paper, we aim to characterize the optimal trade-off between user cache memory and communication load for such systems. First, we propose a novel approach of cache-aided interference alignment (CIA) , for the MuPIR problem with $K=2$ messages, $K_{\mathrm{ u}}=2$ users and $N\ge 2$ databases. The CIA approach is optimal when the cache placement is uncoded. For general cache placement, the CIA approach is optimal when $N=2$ and 3 verified by the computer-aided converse approach. Second, for the general case, we propose a product design (PD) which incorporates the PIR code into the linear caching code. The product design is shown to be order optimal within a multiplicative factor of 8 and is exactly optimal in the high memory regime.

中文翻译：

---

缓存辅助多用户隐私信息检索的基本限制

我们考虑缓存辅助多用户隐私信息检索 (MuPIR) 问题，它是单用户缓存辅助 PIR 问题在多用户情况下的扩展。在缓存辅助的 MuPIR 中，每个 $K_{\mathrm{ u}}$ 配备缓存的用户希望私下检索消息 $K$ 来自 $N$ 每个数据库都可以访问整个消息库。需求隐私要求任何单个数据库都不了解所有用户的需求。用户通过无错误的共享链接连接到每个数据库。在本文中，我们旨在表征此类系统的用户缓存和通信负载之间的最佳权衡。首先，我们提出了一种新的方法缓存辅助干扰对齐 (CIA) ，用于 MuPIR 问题 $K=2$ 消息， $K_{\mathrm{ u}}=2$ 用户和 $N\ge 2$ 数据库。当缓存放置未编码时，CIA 方法是最佳的。对于一般缓存放置，CIA 方法是最佳的： $N=2$ 和 3 通过计算机辅助逆向方法验证。其次，对于一般情况，我们提出一个将 PIR 代码合并到线性缓存代码中的产品设计 (PD)。产品设计被证明在 8 倍乘因子内是阶最优的，并且在高内存状态下完全是最优的。