  We consider a cooperative X-channel with $\sf K$ transmitters (TXs) and $\sf
K$ receivers (Rxs) where Txs and Rxs are gathered into groups of size $\sf r$
respectively. Txs belonging to the same group cooperate to jointly transmit a
message to each of the $\sf K- \sf r$ Rxs in all other groups, and each Rx
individually decodes all its intended messages. By introducing a new
interference alignment (IA) scheme, we prove that when $\sf K/\sf r$ is an
integer the sum Degrees of Freedom (SDoF) of this channel is lower bounded by
$2\sf r$ if $\sf K/\sf r \in \{2,3\}$ and by $\frac{\sf K(\sf K-\sf r)-\sf
r^2}{2\sf K-3\sf r}$ if $\sf K/\sf r \geq 4$. We also prove that the SDoF is
upper bounded by $\frac{\sf K(\sf K-\sf r)}{2\sf K-3\sf r}$. The proposed IA
scheme finds application in a wireless distributed MapReduce framework, where
it improves the normalized data delivery time (NDT) compared to the state of
the art.
