Optimal Uncoded Placement and File Grouping Structure for Improved Coded Caching under Nonuniform Popularity

This paper considers the caching design for coded caching under nonuniform file popularity. We investigate the optimal cache placement for the modified coded caching scheme (MCCS) recently proposed with an improved delivery strategy for rate reduction over the original coded caching scheme (CCS). We use the optimization framework for the cache placement problem to minimize the average delivery rate. Exploring several properties of the optimization problem and analyzing its structure, we obtain the file grouping structure under the optimal cache placement. 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 placement solution in these three possible file group cases. Following these, we develop a simple algorithm to obtain the final optimal cache placement solution, which only requires to compute a set of candidate solutions in closed-form. Simulation verifies the optimal solution produced by our algorithm. The optimal MCCS is shown to outperform existing schemes for both MCCS and CCS.