Hierarchical Modulation to Support Low-Density Parity-Check Code Design?

We study variable node degree distributions resulting from a linear programming approach for designing a lowdensity parity-check (LDPC) code optimized for an irregular modulation alphabet. We opt for an irregular LDPC code and make use of the irregularities of the channel in the sense of different modulation classes originating especially from different distances in a hierarchical modulation signal set. Our aim is to investigate if differences in equivalent binary channels as given by hierarchical modulation signal sets would in any way support resulting variable node degree distributions.