The Robustness of Dirty Paper Coding and The Binary Dirty Multiple Access Channel with Common Interference

A dirty-paper channel is considered, where the transmitter knows the interference sequence up to a constant multiplicative factor, known only to the receiver. Lower bounds on the achievable rate of communication are derived by proposing a coding scheme that partially compensates for the imprecise channel knowledge. We focus on a communication scenario where the signalto-noise ratio is high. Our approach is based on analyzing the performance achievable using lattice-based coding schemes. When the power of the interference is finite, we show that the achievable rate of this lattice-based coding scheme may be improved by a judicious choice of the scaling parameter at the receiver. We further show that the communication rate may be improved, for finite as well as infinite interference power, by allowing randomized scaling at the transmitter. This scheme and its analysis are used to compare the performance of linear and dirty paper coding transmission techniques over the MIMO broadcast channel, in the presence of channel uncertainty. We also consider a binary dirty multiple-access channel with interference known at both encoders. We derive an achievable rate region for this channel which contains the sum-rate capacity and observe that the sum-rate capacity in this setup coincides with the capacity of the channel when full-cooperation is allowed between transmitters, contrary to the analogous Gaussian case.