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We consider a cooperative X-channel with $\sf K$ transmitters (TXs) and $\sfK$ 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 amessage to each of the $\sf K- \sf r$ Rxs in all other groups, and each Rxindividually decodes all its intended messages. By introducing a newinterference alignment (IA) scheme, we prove that when $\sf K/\sf r$ is aninteger 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 $\frac{\sf K(\sf K-\sf r)-\sfr^2}{2\sf K-3\sf r}$ if $\sf K/\sf r \geq 4$. We also prove that the SDoF isupper bounded by $\frac{\sf K(\sf K-\sf r)}{2\sf K-3\sf r}$. The proposed IAscheme finds application in a wireless distributed MapReduce framework, whereit improves the normalized data delivery time (NDT) compared to the state ofthe art.

DoF of a Cooperative X-Channel with an Application to Distributed Computing