On Rate Region of Caching Problems With Non-Uniform File and Cache Sizes

Rate region of the caching problems with non-uniform file and cache sizes can be characterized in terms of the region of entropic vectors, which is unknown in general. One can replace the region of entropic vectors with its polyhedral outer bound to get the associated outer bound on the rate region. A new computation method is introduced for the calculation. The polyhedral projection is converted into a multiple objective linear programming and an implementation of Benson's outer approximation algorithm is used to solve it. As a demonstration, rate region of the two-file two-user caching problem is calculated and proved to be binary codes sufficient.