  The connection between index coding and matroid theory have been well studied
in the recent past. El Rouayheb et al. established a connection between multi
linear 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. We show that vector linear differential error
correcting index code exists if and only if there exists a representable
discrete polymatroid satisfying certain conditions
