Probabilistic constellation shaping (PCS) is applied to a desired probability distribution over the 2-D constellation points. Constellation points are partitioned into multiple disjoint sets in which all the constellation points within a subset have the same energy level (i.e., amplitude) or distance from the origin on the complex plane. Each of the sets may be further subdivided into smaller disjoint sets of constellation points to facilitate labeling of the constellation points. The sets may be indexed from 0 to the total number of disjoint sets to form an index set. The desired distribution may then be applied over the index set either using a distribution matcher (DM) or using a lookup table. The desired distribution may be generated before forward error correction (FEC) encoding that preserves the generated amplitude distribution through FEC encoding of data bits. The scheme may map the FEC encoded data bits to the constellation points, such that the probability of occurrence of each signal set (with a specific energy level) follows the desired probability distribution within a fixed codeword length. In addition, PCS can be applied to both square and non-square constellations, which may or may not be arranged on a Cartesian grid.