Probabilistic shaping is a research area in information theory and digital communication that focuses on using probabilistic methods to optimize the shaping of data before transmission. The goal of probabilistic shaping is to improve the efficiency and reliability of communication systems by carefully designing the probability distribution of transmitted symbols. By shaping the data in this way, it is possible to minimize transmission errors and improve overall system performance. Probabilistic shaping is used in a variety of communication systems, including optical communication, wireless communication, and digital broadcasting.