Probabilistic Shaping and its Applications for Optical Communications

Abstract

Communication channels often have non-uniform capacity-achieving input distributions (see Fig 1 for an example distribution). This has been the main motivation for probabilistic shaping (PS), i.e., the development of practical transmission schemes that use non-uniform distributions at the input of the channel. Many different PS schemes have been proposed, see, e.g., the literature review in [1, Section II], An important milestone for making PS practical was the invention of probabilistic amplitude shaping (PAS) [1], which concatenates a shaping outer code called a distribution matcher (DM) [2] and a forward error correction (FEC) inner code, see Fig. 1. The PAS architecture has three properties that distinguishes it from other proposed PS schemes. First, it integrates shaping with existing FEC, second, it achieves the Shannon limit, third, it adapts its rate by changing the probability distribution, while leaving the FEC part unchanged. Because of these three properties, PAS plays an important role in coherent optical transmission systems. The benefits of PAS were first demonstrated in optical transmission experiments [3] and then confirmed in field trials [4], [5].