  Index coding studies multiterminal source-coding problems where a set of
receivers are required to decode multiple (possibly different) messages from a
common broadcast, and they each know some messages a priori. In this paper, at
the receiver end, we consider a special setting where each receiver knows only
one message a priori, and each message is known to only one receiver. At the
broadcasting end, we consider a generalized setting where there could be
multiple senders, and each sender knows a subset of the messages. The senders
collaborate to transmit an index code. This work looks at minimizing the number
of total coded bits the senders are required to transmit. When there is only
one sender, we propose a pruning algorithm to find a lower bound on the optimal
(i.e., the shortest) index codelength, and show that it is achievable by linear
index codes. When there are two or more senders, we propose an appending
technique to be used in conjunction with the pruning technique to give a lower
bound on the optimal index codelength; we also derive an upper bound based on
cyclic codes. While the two bounds do not match in general, for the special
case where no two distinct senders know any message in common, the bounds
match, giving the optimal index codelength. The results are expressed in terms
of strongly connected components in directed graphs that represent the
index-coding problems.
