  This paper deals with embedded index coding problem (EICP), introduced by A.
Porter and M. Wootters, which is a decentralized communication problem among
users with side information. An alternate definition of the parameter minrank
of an EICP, which has reduced computational complexity compared to the existing
definition, is presented. A graphical representation for an EICP is given using
directed bipartite graphs, called bipartite problem graph, and the side
information alone is represented using an undirected bipartite graph called the
side information bipartite graph. Inspired by the well-studied single unicast
index coding problem (SUICP), graphical structures, similar to cycles and
cliques in the side information graph of an SUICP, are identified in the side
information bipartite graph of a single unicast embedded index coding problem
(SUEICP). Transmission schemes based on these graphical structures, called tree
cover scheme and bi-clique cover scheme are also presented for an SUEICP. Also,
a relation between connectedness of the side information bipartite graph and
the number of transmissions required in a scalar linear solution of an EICP is
established.
