In this project, we investigate the effect of using multilevel signaling with coded modulation techniques for fiber-optical communication systems with optical amplifiers. Such systems are usually dominated by the beat noise of amplified spontaneous emission. After square-root transforming the received signal, we apply the coded modulation schemes such as trellis-coded modulation and multi-level coding, which lead to significant power gain. Further improvements are made by jointly optimizing the coded modulation and the signal constellation.
In this project, we study the theory of lattice code shaping and nonequiprobable signaling for optical systems. Previous work has established results for coherent detection systems  and direct-detection systems without amplifiers .
Our work focuses on the theory of shaping and nonequiprobable signaling for amplified direct-detection systems. In such systems, the intensity-modulated signals are corrupted by the signal-spontaneous emission beat noise, which is proportional to the signal intensity.