Demand Private Coded Caching: the Two-File Case
Qinyi Lu, Nan Liu, Wei Kang
TL;DR
The paper tackles demand-private coded caching in a $(N,K)$ system, introducing a virtual-user based approach that adapts the YMA scheme to enforce demand privacy. It establishes a new achievable memory-rate tradeoff for arbitrary $(N,K)$ and proves new converses in the two-file setting, enabling exact characterizations. Specifically, it yields the exact tradeoff for the 2-file, 3-user case and provides exact results for 2 files with general $K$ within two cache regimes, $M otin( rac{2}{K}, rac{2(K-1)}{K+1})$, expressed in closed forms. These results advance understanding of privacy-preserving coded caching with finite files and caches and lay groundwork for broader privacy-constrained caching designs.
Abstract
We investigate the demand private coded caching problem, which is an $(N,K)$ coded caching problem with $N$ files, $K$ users, each equipped with a cache of size $M$, and an additional privacy constraint on user demands. We first present a new virtual-user-based achievable scheme for arbitrary number of users and files. Then, for the case of 2 files and arbitrary number of users, we derive some new converse bounds. As a result, we obtain the exact memory-rate tradeoff of the demand private coded caching problem for 2 files and 3 users. As for the case of 2 files and arbitrary number of users, the exact memory-rate tradeoff is characterized for $M\in [0,\frac{2}{K}] \cup [\frac{2(K-1)}{K+1},2]$.