Degrees of freedom region for an interference network with general message demands

We consider a single hop interference network with K transmitters, each with an independent message and J receivers, all having the same number (M) of antennas. Each receiver requests an arbitrary subset of the messages. This generalizes the well-known K user M antenna interference channel, where each message is requested by a unique receiver. For this setup, we derive the exact degrees of freedom (DoF) region. Our achievability scheme generalizes the interference alignment scheme proposed by Cadambe and Jafar '08. In particular, we achieve general points in the DoF region by using multiple base vectors and aligning the interference at each receiver to its largest (in the DoF sense) interferer. As a byproduct of our analysis, we recover the DoF region for the original interference channel.