Characterizing the Optimal Memory-Rate Tradeoff in Secure Coded Caching for Small Buffer or Small Rate
Han Fang, Nan Liu, Wei Kang
TL;DR
This work advances secure coded caching by presenting three new schemes that improve the memory-rate performance under security constraints, and by deriving novel converses that tighten the endpoints of the optimal memory-rate tradeoff. It characterizes the end-points of the tradeoff for arbitrary numbers of files $N$ and users $K$, and provides a small-cache segment result for the two-file case $N=2$. The achievability results rely on linear schemes with randomness optimization and, in the $M>1,R>1$ regime, on non-standard secret sharing combined with Vandermonde constructions to reduce randomness overhead. The converse analyses leverage deterministic-delivery-content properties and symmetry arguments to establish tighter lower bounds than prior work, leading to a fuller understanding of the secure caching landscape and its practical implications for cache-aided networks.
Abstract
We consider the secure coded caching problem proposed by Ravindrakumar et. al where no user can obtain information about files other than the one requested. We first propose three new schemes for the three cases of cache size $M=1$, $N=2$ files and arbitrary $K$ users, delivery rate $ R=1$, arbitrary $N$ files and $K$ users, and the general case for arbitrary $N$ files and $K$ users, respectively. Then we derive converse results by characterizing new properties of secure coded caching schemes. As a result, we characterize the two end-points of the optimal memory-rate tradeoff curve for arbitrary number of users and files. Furthermore, for the case of $N=2$ files and arbitrary number of users, we also characterize a segment of the optimal memory-rate tradeoff curve, where the cache size is relatively small.