Precoding for Channels with Discrete Interference

M -ary signal transmission over AWGN channel with additive Q-ary 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 MQ − Q + 1 out of M Q 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 this setting, the general structure of a communication system with optimal precoding is proposed.