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：我们考虑在隐私约束下具有多个需求的编码缓存问题。在该问题中，服务器可访问 \(N\) 个文件，通过共享链路服务 \(K\) 个用户，每个用户请求 \(L\) 个互不相同的文件。隐私约束要求每个用户无法获取其他用户需求的任何信息。针对任意数量的文件和用户，我们提出了一种新的可实现方案。该方案通过对 \(N\) 个文件、\(K \cdot \min\{N,KL\}\) 个用户（每个用户请求一个文件，且需求局限于所有可能需求的子集）在非编码放置下的非隐私编码缓存方案进行变换而获得。随后我们推导了一个逆界，并证明所提方案在该逆界的6倍因子内达到阶最优。