Analysis and Design of Dirty Paper Coding by Transformation of Noise

We design a coding scheme for Costa´s dirty paper coding (DPC) (M.H.M. Costa, 1983) using a channel and a shaping code. We show that by transforming the channel noise distribution the DPC channel can be converted into the binary erasure channel (BEC) with binary interference with memory. Furthermore, the messages exchanged during the iterative decoding between the channel and shaping codes become one dimensional under the new model. We analyze the iterative decoding and find good shaping and channel code pairs using some closed-form extrinsic information transfer (EXIT) curves. We verify that our dirty paper codes designed using this method are also good for the original DPC channel with the additive white Gaussian noise (AWGN) and arbitrary interference. Our implementation of DPC uses short block codes such as repetition codes for shaping codes. Although the shaping gains of such codes are not very high, they may provide a better complexity-performance trade-off for simple practical implementations of DPC. Furthermore, we show accurate theoretical analysis is possible for such codes under our channel model.