Fundamental Limits of Caching for Demand Privacy against Colluding Users
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This work investigates the problem of demand privacy against colluding users for shared-link coded caching systems, where no subset of users can learn any information about the demands of the remaining users. The notion of privacy used here is stronger than similar notions adopted in past work and is motivated by the practical need to insure privacy regardless of the file distribution. This paper provides both an achievable scheme, referred to as Linear Function Retrieval for Demand Privacy against Colluding Users (LFR-DPCU), and a novel information theoretic converse bound. By comparing the performance of the achievable scheme with the converse bound derived in this paper (for the small cache size regime) and existing converse bounds without privacy constraints, the communication load of LFR-DPCU turns out to be optimal to within a constant multiplicative gap in all parameter regimes. Numerical results show that LFR-DPCU outperforms known schemes based on the idea of virtual users, which also satisfy the stronger notion of user privacy adopted here, in some regime. Moreover, LFR-DPCU enjoys much lower subpacketization than known schemes based on virtual users.
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