  Information theoretic analysis of a coded caching system is considered, in
which a server with a database of N equal-size files, each F bits long, serves
K users. Each user is assumed to have a local cache that can store M files,
i.e., capacity of MF bits. Proactive caching to user terminals is considered,
in which the caches are filled by the server in advance during the placement
phase, without knowing the user requests. Each user requests a single file, and
all the requests are satisfied simultaneously through a shared error-free link
during the delivery phase.
  First, centralized coded caching is studied assuming both the number and the
identity of the active users in the delivery phase are known by the server
during the placement phase. A novel group-based centralized coded caching (GBC)
scheme is proposed for a cache capacity of M = N/K. It is shown that this
scheme achieves a smaller delivery rate than all the known schemes in the
literature. The improvement is then extended to a wider range of cache
capacities through memory-sharing between the proposed scheme and other known
schemes in the literature. Next, the proposed centralized coded caching idea is
exploited in the decentralized setting, in which the identities of the users
that participate in the delivery phase are assumed to be unknown during the
placement phase. It is shown that the proposed decentralized caching scheme
also achieves a delivery rate smaller than the state-of-the-art. Numerical
simulations are also presented to corroborate our theoretical results.
