Coded Caching Under Arbitrary Popularity Distributions

Caching plays an important role in reducing the backbone traffic when serving high-volume multimedia content. Recently, a new class of coded caching schemes have received significant interest, because they can exploit coded multi-cast opportunities to further reduce backbone traffic. Without considering file popularity, prior works have characterized the fundamental performance limits of coded caching through a deterministic worst-case analysis. However, when heterogeneous file popularity is considered, there remain open questions regarding the fundamental limits of coded caching performance. In this paper, for an arbitrary popularity distribution, we first derive a new information-theoretic lower bound on the expected transmission rate of any coded caching schemes. We then show that a simple coded-caching scheme attains an expected transmission rate that is at most a constant factor away from the lower bound. Unlike other existing studies, the constant factor that we derived is independent of the popularity distribution.