  The connection between index coding and matroid theory have been well studied
in the recent past. El Rouayheb et al. established a connection between
multilinear representation of matroids and wireless index coding. Muralidharan
and Rajan showed that a vector linear solution to an index coding problem
exists if and only if there exists a representable discrete polymatroid
satisfying certain conditions. Recently index coding with erroneous
transmission was considered by Dau et al.. Error correcting index codes in
which all receivers are able to correct a fixed number of errors was studied.
In this paper we consider a more general scenario in which each receiver is
able to correct a desired number of errors, calling such index codes
differential error correcting index codes. A link between differential error
correcting index codes and certain matroids is established. We define matroidal
differential error correcting index codes and we show that a scalar linear
differential error correcting index code exists if and only if it is matroidal
differential error correcting index code associated with a representable
matroid.
