Capacity region of a class of strong MIMO IC

The capacity region of a class of 2-user multi-input multi-output (MIMO) strong interference channels (IC) is characterized. As a stepping stone we prove a new upper bound to the difference of two mutual information. This class of channels called strong in partial order channels, generalizes the notion of strong channels introduced earlier in the literature in the context of SISO and SIMO Gaussian interference channels. The class of strong in partial order channels, although have an overlap with the class of aligned-strong ICs introduced by Shang et. al., also contain channels which are not aligned-strong. Further, it is proved that using independent and random Gaussian codes at the transmitters and decoding both users messages at the receivers are sufficient to achieve the capacity region on this class of channels. This result enlarges the set of channels for which exact capacity of the 2-user MIMO Gaussian IC can be characterized.