Memory-Rate Tradeoff for Decentralized Caching under Nonuniform File Popularity.

We study the memory-rate tradeoff for decentralized caching under nonuniform file popularity. We formulate the cache placement optimization problem for a recently proposed decentralized modified coded caching scheme (D-MCCS) to minimize the average rate. To solve this non-convex optimization problem, we develop two algorithms: a successive Geometric Programming (GP) approximation algorithm, which guarantees convergence to a stationary point but has a high computational complexity, and a low-complexity approach based on a two-file-group-based placement strategy. We further propose a lower bound on the average rate for decentralized caching under nonuniform file popularity. The lower bound is given as a nonconvex optimization problem, for which we propose a similar successive GP approximation algorithm to compute a stationary point. We show that the optimized MCCS attains the lower bound for the special case of no more than two active users requesting files, or for the general case but satisfying a special condition. Thus, the optimized MCCS characterizes the exact memory-rate tradeoff for decentralized caching in these cases. In general, our numerical result shows that the optimized D-MCCS performs close to the lower bound.