Demand Private Coded Caching: Small Cache Size

2025-04-25

AI Summary

This paper studies the demand-private coded caching problem: in a system with $N$ files and $K$ users, each user has a cache of size $M$, and strict demand privacy must be guaranteed—i.e., no user may infer any other user’s request. Focusing on the small-cache regime ($M < N/K$), the work fully characterizes the optimal memory–rate trade-off for multiple settings: (i) $N leq K leq 2N-2$, (ii) $K > 2N-2$, (iii) $N = 2$ (for arbitrary $K$), and (iv) $(N,K) = (2,3)$. The key methodological innovation is a joint scheme combining virtual-user construction and maximum-distance separable (MDS) coding, complemented by tight information-theoretic converse bounds derived via novel combinatorial and entropy-based arguments. The proposed scheme achieves these converse bounds across multiple $M$-intervals, thereby establishing optimality. This work significantly advances the fundamental understanding of privacy-preserving edge caching, precisely delineating its theoretical limits under stringent demand privacy constraints.

Technology Category

• Machine Learning: Privacy
• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

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 ig[0, frac{N}{(K+1)(N-1)} ig] $ where $N le K le 2N-2$, and the optimal memory-rate tradeoff for $M in ig[0, frac{1}{K+1} ig] $ 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 $Min ig[0,frac{2}{K}ig] cup ig[frac{2(K-1)}{K+1},2ig]$. Finally, we provide the optimal memory-rate tradeoff of the demand private coded caching problem for 2 files and 3 users.

Problem

• Demand private coded caching with small cache sizes
• Privacy constraints on user demands in caching
• Optimal memory-rate tradeoff characterization

Innovation

• Virtual-user scheme for arbitrary users/files
• MDS-code schemes for N ≤ K cases
• Optimal memory-rate tradeoff characterization