  This paper considers heterogeneous coded caching where the users have unequal
distortion requirements. The server is connected to the users via an error-free
multicast link and designs the users' cache sizes subject to a total memory
budget. In particular, in the placement phase, the server jointly designs the
users' cache sizes and the cache contents. To serve the users' requests, in the
delivery phase, the server transmits signals that satisfy the users' distortion
requirements. An optimization problem with the objective of minimizing the
worst-case delivery load subject to the total cache memory budget and users'
distortion requirements is formulated. The optimal solution for uncoded
placement and linear delivery is characterized explicitly and is shown to
exhibit a threshold policy with respect to the total cache memory budget. As a
byproduct of the study, a caching scheme for systems with fixed cache sizes
that outperforms the state-of-art is presented.
