Coded Caching for Multi-level Popularity and Access
  To address the exponentially rising demand for wireless content, use of caching is emerging as a potential solution. It has been recently established that joint design of content delivery and storage (coded caching) can significantly improve performance over conventional caching. Coded caching is well suited to emerging heterogeneous wireless architectures which consist of a dense deployment of local-coverage wireless access points (APs) with high data rates, along with sparsely-distributed, large-coverage macro-cell base stations (BS). This enables design of coded caching-and-delivery schemes that equip APs with storage, and place content in them in a way that creates coded-multicast opportunities for combining with macro-cell broadcast to satisfy users even with different demands. Such coded-caching schemes have been shown to be order-optimal with respect to the BS transmission rate, for a system with single-level content, i.e., one where all content is uniformly popular. In this work, we consider a system with non-uniform popularity content which is divided into multiple levels, based on varying degrees of popularity. The main contribution of this work is the derivation of an order-optimal scheme which judiciously shares cache memory among files with different popularities. To show order-optimality we derive new information-theoretic lower bounds, which use a sliding-window entropy inequality, effectively creating a non-cutset bound. We also extend the ideas to when users can access multiple caches along with the broadcast. Finally we consider two extreme cases of user distribution across caches for the multi-level popularity model: a single user per cache (single-user setup) versus a large number of users per cache (multi-user setup), and demonstrate a dichotomy in the order-optimal strategies for these two extreme cases. 
Jad Hachem, Nikhil Karamchandani, Suhas Diggavi
cs.IT math.IT