Fundamental Limits of Heterogenous Cache

Recently, a novel technique called coded cache have been proposed to facilitate the wireless content distribution. Assuming the users have the identical cache size, prior works have described the fundamental performance limits of such scheme. However, when heterogenous user cache sizes is taken into account, there remains open questions regarding the performance of the cache. In this work, for the heterogenous user cache sizes, we first derive the information-theoretical lower bound and show that although the traditional coded caching scheme will cause miss of coding opportunities in this regime, it still exhibits the constant gap 6 to the lower bound. To reveal the essence in this result, we introduce the concept of the probabilistic cache set and find the guarantee of such order optimality mainly comes from the intrinsic degenerated efficiency of bottleneck caching network under the heterogenous cache sizes. Moreover, we point out such miss of coding opportunities is caused not only by the heterogenous cache sizes but also by the group coded delivery, which divide users into groups and operate coded cache separately. And the combination of above two schemes will not cumulate this effect, instead, they cancel each other out.