  This paper studies a special class of multicast index coding problems where a
sender transmits messages to multiple receivers, each with some side
information. Here, each receiver knows a unique message a priori, and there is
no restriction on how many messages each receiver requests from the sender. For
this class of multicast index coding problems, we obtain the optimal index
code, which has the shortest codelength for which the sender needs to send in
order for all receivers to obtain their (respective) requested messages. This
is the first class of index coding problems where the optimal index codes are
found. In addition, linear index codes are shown to be optimal for this class
of index coding problems.
