  Coded caching has the potential to greatly reduce network traffic by
leveraging the cheap and abundant storage available in end-user devices so as
to create multicast opportunities in the delivery phase. In the seminal work by
Maddah-Ali and Niesen (MAN), the shared-link coded caching problem was
formulated, where each user demands one file (i.e., single file retrieval).
This paper generalizes the MAN problem so as to allow users to request scalar
linear functions of the files. This paper proposes a novel coded delivery
scheme that, based on MAN uncoded cache placement, is shown to allow for the
decoding of arbitrary scalar linear functions of the files (on arbitrary finite
fields). Interestingly, and quite surprisingly, it is shown that the load for
cache-aided scalar linear function retrieval depends on the number of linearly
independent functions that are demanded, akin to the cache-aided single-file
retrieval problem where the load depends on the number of distinct file
requests. The proposed scheme is optimal under the constraint of uncoded cache
placement, in terms of worst-case load, and within a factor 2 otherwise. The
key idea of this paper can be extended to all scenarios which the original MAN
scheme has been extended to, including demand-private and/or device-to-device
settings.
