Demand Private Coded Caching: Small Cache Size
Qinyi Lu, Nan Liu, Wei Kang, Chunguo Li
TL;DR
This work advances the study of demand-private coded caching under small cache constraints by introducing three novel schemes (one virtual-user-based and two MDS-code-based) and a new information-theoretic converse. By deriving region-specific optimal memory-rate tradeoffs for general N,K (notably N ≤ K and K > 2N−2) and complete results for the case N=2, it tightens the understanding of how privacy constraints reshape the fundamental limits of caching. The virtual-user scheme leverages a mapping from a restricted non-private problem, while the MDS-based schemes use coded placement and random permutations to ensure privacy across diverse demand patterns. The results have practical implications for privacy-preserving content delivery in networks with small caches and varying numbers of users and files.
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, i.e., each user can not gain any information about the demands of other users. We focus on scenarios where the size of users' caches is small, aiming to further characterize the fundamental limits of this problem. We first present a new virtual-user-based achievable scheme for arbitrary number of users and files, and two MDS-code-based achievable schemes for the case $N \le K$. With a newly derived converse bound for the case $N \le K$, these proposed schemes lead to the optimal memory-rate tradeoff of the demand private coded caching problem for $M \in \big[0, \frac{N}{(K+1)(N-1)} \big] $ where $N \le K \le 2N-2$, and the optimal memory-rate tradeoff for $M \in \big[0, \frac{1}{K+1} \big] $ where $ K > 2N-2$. Moreover, for the case of 2 files and arbitrary number of users, by deriving another new converse bound, the optimal memory-rate tradeoff is characterized for $M\in \big[0,\frac{2}{K}\big] \cup \big[\frac{2(K-1)}{K+1},2\big]$. Finally, we provide the optimal memory-rate tradeoff of the demand private coded caching problem for 2 files and 3 users.