A new coding technique, based on \textit{fixed block-length} codes, is
proposed for the problem of communicating a pair of correlated sources over a
$2-$user interference channel. Its performance is analyzed to derive a new set
of sufficient conditions. The latter is proven to be strictly less binding than
the current known best, which is due to Liu and Chen [Dec, 2011]. Our findings
are inspired by Dueck's example [March, 1981]