The MIMO-BC model is as follows. A transmitter with antennas wants to transmit independent information to receivers, where receiver is equipped with antennas . Let be the signal transmitted by the transmitter, then the received signal received by receiver is given by where is a channel matrix and is the additive white Gaussian noise (AWGN) with covariance matrix .

For MIMO-BC, several transmission strategies have been proposed in literature, for example, superposition coding and dirty paper coding. In superposition coding, if is the signal for receiver then is transmitted by the transmitter. Dirty paper coding (DPC) is a technique developed by Costa for single input single output (SISO) AWGN channels when there is an interference signal present at the receiver together with AWGN. We assume the interference signal is known non causally at the transmitter. In this setting Costa showed that the capacity is which is exactly equal to the capacity of AWGN channel without any interference. Thus, DPC is shown to completely eliminate the effect of interference. Using DPC for the MIMO BC, if the signal for the first receiver is , then the signal for receiver is generated using as the interference signal. Similarly, the signal for the receiver is generated using as the interference signals and is transmitted from the transmitter. From now on we consider in this article for simplicity. With ,the rates and , simultaneously achievable for receiver and , are given by and where is the covariance matrix of . Changing the order of coding, i.e. first generating and depending on generating , and We denote the convex hull of all rate vectors achievable with DPC as .

As shown above, finding the achievable rate region of MIMO-BC is easy using different transmission strategies but proving that they are capacity achieving, i.e. rate more than the rate achieved by a particular transmission strategy is not achievable with reliable transmission constraint, is quite difficult. Weingarten et.al. solved this problem in their paper and showed that rates achieved with DPC are optimal for MIMO-BC.