Novel Converse for Device-to-Device Demand-Private Caching with a Trusted Server

This paper considers cache-aided device-to-device (D2D) networks where a trusted server helps to preserve the privacy of the users' demands. Specifically, the trusted server collects the users' demands before the delivery phase and sends a query to each user, who then broadcasts multicast packets according to this query. Recently the Authors proposed a D2D private caching scheme that was shown to be order optimal except for the very low memory size regime, where the optimality was proved by comparing to a converse bound without privacy constraint. The main contribution of this paper is a novel converse bound for the studied model where users may collude (i.e., some users share cache contents and demanded files, and yet cannot infer what files the remaining users have demanded) and under the placement phase is uncoded. To the best of the Author's knowledge, such a general bound is the first that genuinely accounts for the demand privacy constraint. The novel converse bound not only allows to show that the known achievable scheme is order optimal in all cache size regimes (while the existing converse bounds cannot show it), but also has the potential to be used in other variants of demand private caching.