Theoretic results have shown that the capacity of a channel does not decrease if the receiver observes the transmitted signal in the presence of interference, provided that the transmitter knows this interference non-causally. That is, if the transmitter has non-causal access to the interference, by using proper precoding this interference could be “avoided” (as if it were not present) under the same transmit power constraint. It indicates that lossless (in the sense of capacity) precoding is theoretically possible at any signal-to-noise-ratio (SNR). This is of special interest in digital watermarking, transmission for ISI channels as well as for MIMO broadcast channels. Recent research has elegantly demonstrated the (near) achievability of this “existence-type” result, while the complexity is notable. An interesting question is what one can do when very little extra complexity is permitted. This thesis treats such special cases of this problem in order to shed some light on this question. In the AWGN channel with additive interference, an optimum modulator is designed under the constraint of a binary signaling alphabet with binary interference.Tomlinson-Harashima precoding (THP), which is originally proposed for ISI channels, is improved by picking up optimized parameters and then taken as a benchmark. Simulation results show that the Optimum Modulator always outperforms the THP with optimized parameters. The difference in performance, in terms of mutual information between channel input and output as well as coded bit error rate with Turbo codes, is significant in many scenarios.