On the Optimality of "Half the Cake" for K-User Rank-Deficient Mk x Mk Interference Channel

By introducing a novel outer bound, we find a sufficient condition for optimality of $\sum_{k=1}^K M_k/2$ degrees of freedom (half the cake per user) for a $K$-user multiple-input- multiple-output (MIMO) interference channel (IC) where the cross-channels have arbitrary rank constraints, and the $k^{th}$ transmitter and receiver are equipped with $M_k$ antennas each. The result consolidates and significantly generalizes results from prior studies by Krishnamurthy et al., of rank-deficient interference channels where all users have $M$ antennas; and by Tang et al., of full rank interference channels where the $k^{th}$ user pair has $M_k$ antennas.