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The most commonly used setting in the coded caching literature consists of the following four elements: (i) homogeneous file sizes, (ii) homogeneous cache sizes, (iii) user-independent homogeneous file popularity (i.e., all users share the same file preference), and (iv) worst-case rate analysis. While recent results have relaxed some of these assumptions, deeper understanding of the full heterogeneity setting is still much needed since traditional caching schemes place little assumptions on file/cache sizes and almost always allow each user to have his/her own file preference through individualized file request prediction. Taking a microscopic approach, this paper characterizes the exact capacity of the smallest 2-user/2-file (N = K = 2) problem but under the most general setting that simultaneously allows for (i) heterogeneous files sizes, (ii) heterogeneous cache sizes, (iii) user-dependent file popularity, and (iv) average-rate analysis. Solving completely the case of N = K = 2 could shed further insights on the performance and complexity of optimal coded caching with full heterogeneity for arbitrary N and K. 

Coded caching is a technique for reducing congestion in communication networks by prefetching content during idle periods and exploiting multicasting opportunities during periods of heavy traffic. Most of the existing research in this area has focused on minimizing the worst case (i.e., peak) rate in a broadcast link with multiple identically distributed user requests. However, modern content delivery networks are investing very heavily in profiling their users and predicting their preferences. The minimal achievable rate of a coded caching scheme with heterogeneous user profiles is still unknown in general. This paper presents the first steps towards solving that problem by analyzing the case of two users with distinct but overlapping demand sets. Specifically, it provides a complete characterization of the uniform-average-rate capacity when the sets overlap in just one file and shows that such capacity can be achieved with selfish and uncoded prefetching. Then, it characterizes the same capacity under selfish and uncoded prefetching when the demand sets overlap in two or more files. The paper also provides explicit prefetching schemes that achieve those capacities. All our results allow for arbitrary (and not necessarily identical) users’ cache sizes and number of files in each demand set.