  We consider the \emph{functional index coding problem} over an error-free
broadcast network in which a source generates a set of messages and there are
multiple receivers, each holding a set of functions of source messages in its
cache, called the \emph{Has-set}, and demands to know another set of functions
of messages, called the \emph{Want-set}. Cognizant of the receivers'
\emph{Has-sets}, the source aims to satisfy the demands of each receiver by
making coded transmissions, called a \emph{functional index code}. The
objective is to minimize the number of such transmissions required. The
restriction a receiver's demands pose on the code is represented via a
constraint called the \emph{generalized exclusive law} and obtain a code using
the \emph{confusion graph} constructed using these constraints. Bounds on the
size of an optimal code based on the parameters of the confusion graph are
presented. Next, we consider the case of erroneous transmissions and provide a
necessary and sufficient condition that an FIC must satisfy for correct
decoding of desired functions at each receiver and obtain a lower bound on the
length of an error-correcting FIC.
