We consider a coded caching problem with multiple demands under a privacy constraint. In this problem, a server with access to \(N\) files serves \(K\) users over a shared link, and each user requests \(L\) distinct files. The privacy constraint requires that each user obtain no information about the demands of the other users. We propose a new achievable scheme for arbitrary numbers of files and users. The scheme is obtained via a transformation from a non-private coded caching scheme under uncoded placement for \(N\) files and \(K \cdot \min\{N,KL\}\) users, where each user requests one file and the demands are restricted to a subset of all possible demands. We then derive a converse bound, and the proposed scheme is shown to be order optimal within a factor of 6 of this bound.

翻译：我们考虑带隐私约束的多请求编码缓存问题。在该问题中，一台可访问 \(N\) 个文件的服务器通过共享链路为 \(K\) 个用户提供服务，每位用户请求 \(L\) 个不同的文件。隐私约束要求每位用户无法获取其他用户请求的任何信息。我们针对任意文件数和任意用户数提出了一种新的可实现方案。该方案通过将非隐私保护编码缓存方案（基于非编码放置，适用于 \(N\) 个文件和 \(K \cdot \min\{N,KL\}\) 个用户，每位用户请求一个文件且请求被限制在所有可能请求的子集中）进行变换而获得。我们进一步推导了一个逆界，并证明该方案在此逆界的6倍因子范围内达到阶数最优。