Dirty paper coding (DPC) is a technique that allows a transmitter to send information through a communication channel by pre-subtracting interference known to the transmitter. The technique is implemented by precoding the data, which cancels known interference at the transmitter.

DPC can achieve the channel capacity of MIMO broadcast channels without power penalty, i.e., $ \sum_{k=1}^{K} \mathbf{x}_k \leq P $, where $ P $ is the total transmit power, and with receiver requirement that a receiver shall have knowledge of other user interference states.

## Mathematical description Edit

We show the interference channel model and analysis the channel capacity of DPC systems. It is assumed that the interference signal vector is $ \mathbf{s} \sim N(0,QI) $ and the noise signal is $ \mathbf{n} \sim N(0,NI) $. Then, the interference channel can given by

- $ \mathbf{y} = \mathbf{x} + \mathbf{s} + \mathbf{z} $

where $ \mathbf{x} $ is the n-dimensional real vector satisfying the transmit power constraint of $ \frac{1}{n}||\mathbf{x}||^2 \leq P $.