Coded Caching for Two Users with Distinct File Sizes

Coded caching has been studied extensively and extended to many scenarios because it can exploit multicast opportunities to reduce the downlink traffic on the network. The basic model of coded caching is that a server with $N$ files of the same size, is connected to several users with cache size $M$ through a shared link. Prior work [1] has derived the optimal rate-memory tradeoff of this system with the constraint of uncoded prefetching. However, when heterogeneity of file sizes is taken into account, there remains open questions. In this paper, we consider two users and $N$ files with distinct file sizes. When the cache size is large or small compared to the overall file size, i.e., 0 ≤ $M$ ≤ ½ N F1 or $M$ ≥ H(W) - ½ N F1 where $F$1 denotes the minimum file size and H (W) represents the overall information entropy of all files in the database, we show that our proposed scheme is optimal under all possible schemes. When the cache size is mediate, i.e., ½ N F1< $M$ < H(W) - ½ N F1 we show that our proposed scheme is optimal under the constraint of uncoded prefetching. To obtain these results, we introduce new techniques to extend the novel cut-set bound in [2], and propose a new achievable scheme based on both files and caches sizes.