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A Graph Theoretical Analysis of Low-Power Coding Schemes for One-Hop Networks

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.