On Distribution Matching for Probabilistic Constellation Shaping

Distribution matching (DM) transforms a stream of equally likely bits into digital symbols that correspond to a specific digital modulation scheme with probabilities of occurrence following a specified statistical distribution. This technique is referred to as probabilistic constellation shaping (PCS), and using the Maxwell–Boltzmann (MB) distribution improves spectral and energy efficiency of digital modulation schemes by enabling more frequent transmissions of lower energy digital symbols. The background behind PCS is presented in the paper and the two main DM methods widely used in practice are discussed, outlining scenarios in which one DM method may be preferable over the other. For illustration, a 64-QAM digital constellation is considered as a case study for which the two DM scenarios presented are simulated and compared in terms the average signal power, entropy, and rate loss.