Fundamental Structure of Optimal Cache Placement for Coded Caching with Heterogeneous Demands

This paper studies the caching system of multiple cache-enabled users with heterogeneous demands. Under nonuniform file popularity, we thoroughly characterize the structure of the optimal uncoded cache placement for the coded caching scheme (CCS). Formulating the cache placement as an optimization problem to minimize the average delivery rate, we identify the file grouping structure under the optimal solution. We show that, regardless of file popularity, there are at most three file groups under the optimal cache placement. We further characterize the complete structure of the optimal cache placement and obtain the closed-form solution in each possible file grouping case. A simple algorithm is developed to obtain the final optimal cache placement, which only computes a set of candidate closed-form solutions in parallel. We provide insights into the file groups formed by the optimal cache placement. The optimal placement solution also indicates that coding between file groups may be explored during delivery, in contrast to the existing heuristic file grouping schemes. Using the file grouping in the optimal cache placement, we propose a new information-theoretic converse bound for coded caching that is tighter than existing ones. Moreover, using the optimal cache placement solution, we characterize the file subpacketization in the optimal CCS and show that the maximum subpacketization level in the worst case scales as $\mathcal{O}(2^K/\sqrt{K})$ for $K$ users.Comment: 19 pages, 12 figures, submitted to IEEE Trans. Information Theor

Uncoded Caching and Cross-level Coded Delivery for Non-uniform File Popularity

Proactive content caching at user devices and coded delivery is studied considering a non-uniform file popularity distribution. A novel centralized uncoded caching and coded delivery scheme, which can be applied to large file libraries, is proposed. The proposed cross-level coded delivery (CLCD) scheme is shown to achieve a lower average delivery rate than the state of art. In the proposed CLCD scheme, the same subpacketization is used for all the files in the library in order to prevent additional zero-padding in the delivery phase, and unlike the existing schemes in the literature, two users requesting files from different popularity groups can be served by the same multicast message in order to reduce the delivery rate. Simulation results indicate significant reduction in the average delivery rate for typical Zipf distribution parameter values.Comment: A shorter version of this paper has been presented at IEEE International Conference on Communications (ICC) 201