  This work studies the coded caching problem in a setting where the users are
simultaneously endowed with a private cache and a shared cache. The setting
consists of a server connected to a set of users, assisted by a smaller number
of helper nodes that are equipped with their own storage. In addition to the
helper cache, each user possesses a dedicated cache which is also used to
prefetch file contents. Each helper cache can serve an arbitrary number of
users, but each user gets served by only one helper cache. We consider two
scenarios: (a) the server has no prior information about the user-to-helper
cache association, and (b) the server knows the user-to-helper cache
association at the placement phase itself. We design centralized coded caching
schemes under uncoded placement for the above two settings. For case (b), two
schemes are proposed that are optimal in certain memory regimes. Further, a
cut-set based lower bound is derived and used to show that one of the proposed
schemes for case (b) is optimal in certain memory regime.
