  In this paper, it is shown that the rank function of a matroid can be
represented by a "mutual information function" if and only if the matroid is
binary. The mutual information function considered is the one measuring the
amount of information between the inputs (binary uniform) and the output of a
multiple access channel (MAC). Moreover, it is shown that a MAC whose mutual
information function is integer valued is "equivalent" to a linear
deterministic MAC, in the sense that it essentially contains at the output no
more information than some linear forms of the inputs. These notes put emphasis
on the connection between mutual information functionals and rank functions in
matroid theory, without assuming prior knowledge on these two subjects. The
first section introduces mutual information functionals, the second section
introduces basic notions of matroid theory, and the third section connects
these two subjects. It is also shown that entropic matroids studied in the
literature correspond to specific cases of MAC matroids.
