DoF of a Cooperative X-Channel with an Application to Distributed Computing
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We consider a cooperative X-channel with K transmitters (TXs) and K receivers (Rxs) where Txs and Rxs are gathered into groups of size r respectively. Txs belonging to the same group cooperate to jointly transmit a message to each of the K- 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 K/ r is an integer the sum Degrees of Freedom (SDoF) of this channel is lower bounded by 2 r if K/ r ∈{2,3} and by K( K- r)- r^2/2 K-3 r if K/ r ≥ 4. We also prove that the SDoF is upper bounded by K( K- r)/2 K-3 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.
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