Exploring the connection between matroids and network coding theory

Matroids, which are mathematical structures describing a generalized notion of independence, have provided valuable insight toward network coding theory due to similarities between the two. This paper, which is aimed at those potentially unfamiliar with network coding theory or matroids, provides an expository summary of one construction method of an information network from a matroid along with new applications of this construction method. The matroids used in the construction provide examples that elucidate how the properties of a matroid dictate the behavior the information network. Using these examples, we characterize and discuss the implications of the connection between matroids and network coding theory using this construction method.