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.