  Centralized coded caching of popular contents is studied for users with
heterogeneous distortion requirements, corresponding to diverse processing and
display capabilities of mobile devices. Users' distortion requirements are
assumed to be fixed and known, while their particular demands are revealed only
after the placement phase. Modeling each file in the database as an independent
and identically distributed Gaussian vector, the minimum delivery rate that can
satisfy any demand combination within the corresponding distortion target is
studied. The optimal delivery rate is characterized for the special case of two
users and two files for any pair of distortion requirements. For the general
setting with multiple users and files, a layered caching and delivery scheme,
which exploits the successive refinability of Gaussian sources, is proposed.
This scheme caches each content in multiple layers, and it is optimized by
solving two subproblems: lossless caching of each layer with heterogeneous
cache capacities, and allocation of available caches among layers. The delivery
rate minimization problem for each layer is solved numerically, while two
schemes, called the proportional cache allocation (PCA) and ordered cache
allocation (OCA), are proposed for cache allocation. These schemes are compared
with each other and the cut-set bound through numerical simulations.
