Structure of Optimal Cache Placement for Coded Caching with Heterogeneous Demands
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For a caching system of a service provider and multiple cache-enabled users, we investigate the optimal cache placement for the coded caching scheme (CCS) under heterogeneous file demands. Existing works propose heuristic file grouping strategies, leading to suboptimal cache placements. We formulate the cache placement problem for the CCS into an optimization problem to minimize the average rate, for any file popularity distributions and cache size. Through problem reformulation and by exploring the properties of the problem, we obtain the structure of the optimal cache placement. We discover that the optimal cache placement results in at most three file groups. Through analysis, we present the complete structure of the optimal cache placement under each possible file group case and derive a closed-form cache placement solution in each of these cases. Following these results, the optimal cache placement solution can be obtained efficiently. Simulation verifies the optimal cache placement structure and solution, and provides a comparison to existing strategies.
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