Multi-level coded caching

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Abstract
Recent work has demonstrated that, for content caching, joint design of storage and delivery can yield significant benefits over conventional caching approaches. This is based on storing content in the caches in a way that creates coded-multicast opportunities even among users with different demands. Such a coded-caching scheme has been shown to be order-optimal for a caching system with single-level content, i.e., one where all content is uniformly popular. In this work, we consider a system with content divided into multiple levels, based on varying degrees of popularity. The main contribution of this work is the derivation of an information-theoretic outer bound for the multi-level setup, and the demonstration that, under some natural regularity conditions, a memory-sharing scheme, which operates each level in isolation according to a single-level coded caching scheme, is in fact order-optimal with respect to this outer bound.