Design of Dirty Paper Codes for Wireless Broadcast Channels

“Writing on Dirty Paper” is a paper written by M. Costa in 1983 that dealt with the channel capacity when the interference is known only to the transmitter. The conclusion of that paper was that when one wants to write a message on a dirty paper, because the dirt spots are known, one could find a special way to write and convey the message as if the message was written on a clean paper. In information-theoretic terminology, the capacity of a channel with interference known to the transmitter is the same as the clean channel capacity. Recently, with the new developments in applications such as high speed downlink broadcast (for wireless systems, as well as for digital subscriber lines) and multi-media information hiding and watermarking, there has been a resurgence of interest in Costa’s “Dirty Paper Coding (DPC)”. The general view is that DPC allows interference cancellation at transmitter which resembles decisionfeedback detection at receiver. Thus, conventional detection techniques at receiver can be moved to the transmitter if interference and channel side information are known to it. The advantages of doing so are prevention of error propagation in detection and, in the case of practical downlink broadcast, relieving the mobile receivers of complicated detection. Practical approaches to the design of DPC, however, were not available until 2000 when Erez, Shamai and Zamir established the connection between DPC and Tomlinson-Harashima precoding (THP) for channels with intersymbol interference. In their work, Erez et al showed that there is a “shaping loss” in capacity associated with the conventional THP approach. To recover the shaping loss, higher dimensional equivalent of the THP can be used, but the coding complexity is usually high. In addition, THP applies only to cubic constellations which incur a further shaping loss. In this paper, we consider the design of DPC for wireless broadcast channels. In order to reduce the high dimensional precoding and shaping complexity, Eyuboglu and Forney’s trellis precoding and shaping approach will be adopted. It will be shown that combined trellis DPC and shaping is feasible and indeed retains the clean channel performance