  Coding schemes with extremely low computational complexity are required for
particular applications, such as wireless body area networks, in which case
both very high data accuracy and very low power-consumption are required
features. In this paper, coding schemes arising from incidence matrices of
graphs are proposed. An analysis of the resilience of such codes to erasures is
given using graph theoretical arguments; decodability of a graph is
characterized in terms of the rank of its incidence matrix. Bounds are given on
the number of decodable subgraphs of a graph and the number of edges that must
be deleted in order to arrive at an undecodable subgraph. Algorithms to
construct codes that are optimal with respect to these bounds are presented.
