Characterizing the rate-memory tradeoff in cache networks within a factor of 2

We consider a basic caching system, where a single server with a database of N files (e.g. movies) is connected to a set of K users through a shared bottleneck link. Each user has a local cache memory with a size of M files. The system operates in two phases: a placement phase, where each cache memory is populated up to its size from the database, and a following delivery phase, where each user requests a file from the database, and the server is responsible for delivering the requested contents. The objective is to design the two phases to minimize the load (peak or average) of the bottleneck link. We characterize the rate-memory tradeoff of the above caching system within a factor of 2.00884 for both the peak rate and the average rate (under uniform file popularity), where the best proved characterization in the current literature gives a factor of 4 and 4.7 respectively. Moreover, in the practically important case where the number of files (N) is large, we exactly characterize the tradeoff for systems with no more than 5 users, and characterize the tradeoff within a factor of 2 otherwise. We establish these results by developing novel information theoretic outer-bounds for the caching problem, which improves the state of the art and gives tight characterization in various cases.