Matroidal Entropy Functions: Constructions, Characterizations and Representations

Abstract

Matroidal entropy functions are entropy functions in the form $\mathbf{h}=\log v\cdot {\mathbf{r}}_M$ , where $v\ge 2$ is an integer and ${\mathbf{r}}_M$ is the rank function of a matroid $M$. They can be applied into capacity characterization and code construction of information theory problems such as network coding, secret sharing, index coding and locally repairable code. In this paper, by constructing the variable strength arrays of some matroid operations, we characterized matroidal entropy functions induced by regular matroids and some matroids with the same p-characteristic set as uniform matroid $U_{2,4}$.

13 pages, 3 figures, accepted by IEEE Transactions on Information Theory