Precoding for channels with two-level interference

M-ary signal transmission over AWGN channel with additive two-level interference where the sequence of i.i.d. interference symbols is known causally at the transmitter is considered. Shannon’s theorem for channels with side information at the transmitter is used to formulate the capacity of the channel. It is shown that by using at most 2M − 1 out of M 2 inputs of the associated channel the capacity is achievable. We consider the maximization of the transmission rate over input probability assignments for the associated channel that induce uniform distribution on the input to the actual channel, for which we show that by using exactly M out of M 2 inputs of the associated channel the maximum is achievable. Based on this, the general structure of a communication system with optimal precoding is proposed