  We focus on the following instance of an index coding problem, where a set of
receivers are required to decode multiple messages, whilst each knows one of
the messages a priori. In particular, here we consider a generalized setting
where they are multiple senders, each sender only knows a subset of messages,
and all senders are required to collectively transmit the index code. For a
single sender, Ong and Ho (ICC, 2012) have established the optimal index
codelength, where the lower bound was obtained using a pruning algorithm. In
this paper, the pruning algorithm is simplified, and used in conjunction with
an appending technique to give a lower bound to the multi-sender case. An upper
bound is derived based on network coding. While the two bounds do not match in
general, for the special case where no two senders know any message bit in
common, the bounds match, giving the optimal index codelength. The results are
derived based on graph theory, and are expressed in terms of strongly connected
components.
