Optimization-based Decentralized Coded Caching for Files and Caches with Arbitrary Sizes

Existing decentralized coded caching solutions cannot guarantee small loads in the general scenario with arbitrary file sizes and cache sizes. In this paper, we propose an optimization framework for decentralized coded caching in the general scenario to minimize the worst-case load. Specifically, we first propose a class of decentralized coded caching schemes which are specified by a general caching parameter (enabling efficient and flexible placement strategies) and include several known schemes as special cases. Then, we optimize the caching parameter to minimize the worst-case load in the general scenario. The optimization problem is a challenging non-convex problem with a non-differentiable objective function. We develop an iterative algorithm to obtain a stationary point using techniques for solving Complementary Geometric Programming (GP). We also obtain a low-complexity solution by solving an approximate problem with a differentiable objective function which is an upper bound of the original non-differentiable one, and characterize the performance loss caused by the approximation. In addition, we present an information-theoretic converse bound on the worst-case load in the general scenario, extending the existing one for the special case. To the best of our knowledge, this is the first work providing optimization-based decentralized coded caching solutions and the information-theoretic converse bound in the general scenario.