An efficient addressing scheme for shaping of multi-dimensional signal constellations using a lookup table

The paper describes a lookup table for the addressing of an optimally shaped constellation. The method is based on partitioning the subconstellations into shaping macro-shells of integer bit rate and increasing average energy. A lookup table is used to select a subset of the partitions in the cartesian product space. By devising appropriate partitioning/merging rules, the author obtains suboptimum schemes of very low addressing complexity and small performance degradation. The performance is computed using weight distribution of an optimally shaped constellation.