Degrees of Freedom for multiple-multicast traffic

We propose a new coding scheme for interference alignment in a single hop fast fading wireless network with general message demands. For the X-Channel, the Degrees of Freedom (DoF) region achievable by the scheme is shown to touch a known outer-bound at several points. For multiple-multicast demands we show that the achievable region is at least half of the cut-set bound region. The key innovation in our scheme is the reduction of the vector space alignment problem to a combinatorial arrangement problem. Finally, we use the scheme to give a poly-logarithmic bound for the flow-cut gap in fast fading Gaussian wireless networks with multiple multicasts.