On the Rate-Memory Tradeoff of D2D Coded Caching with Three Users

The device-to-device (D2D) centralized coded caching problem is studied for the three-user scenario, where two models are considered. One is the 3-user D2D coded caching model proposed by Ji et al, and the other is a simpler model named the 3-user D2D coded caching with two random requesters and one sender (2RR1S), proposed in this paper, where in the delivery phase, any two of the three users will make file requests, and the user that does not make any file request is the designated sender. We allow for coded cache placement and none one-shot delivery schemes. We first find the optimal caching and delivery schemes for the model of the 3-user D2D coded caching with 2RR1S for any number of files. Next, we propose a new caching and delivery scheme for the 3-user D2D coded caching problem using the optimal scheme of the 3-user D2D coded caching with 2RR1S as a base scheme. The new caching and delivery scheme proposed employs coded cache placement and when the number of files is equal to 2 and the cache size is medium, it outperforms existing schemes which focus on uncoded cache placement. We further characterize the optimal rate-memory tradeoff for the 3-user D2D coded caching problem when the number of files is equal to 2. As a result, we show that the new caching and delivery scheme proposed is in fact optimal when the cache size is in the medium range.Comment: To be submitted for possible journal publicatio

Fundamental Limits of Device-to-Device Private Caching with a Trusted Server under Uncoded Cache Placement and User Collusion

In the coded caching problem, as originally formulated by Maddah-Ali and Niesen, a server communicates via a noiseless broadcast link to multiple users that have local storage capability. In order for a user to decode the desired file from the coded multicast transmission, the demands of all the users must be globally known, which may violate the privacy of the users. To overcome this privacy problem, Wan and Caire recently proposed several schemes that attain coded multicasting gain while simultaneously guarantee information theoretic privacy of the users' demands. In Device-to-Device (D2D) networks, the demand privacy problem is further exacerbated by the fact that each user is also a transmitter, which should know the files demanded by the remaining users in order to form its coded multicast transmissions. This paper solves this seemingly infeasible problem with the aid of a trusted server. Specifically, during the delivery phase, the trusted server collects the users' demands and sends a query to each user, who then broadcasts coded multicast packets according to this query. The main contribution of this paper is the development of novel achievable schemes and converse bounds for D2D private caching with a trusted server, where users may be colluding (i.e., when some users share cached content and demanded file indices), that are to within a constant factor of one another.Comment: 64 pages, 6 figures, under review of TIT, parts of results were presented in ICC 2020 and ISIT 202