Two-Stage Dimension-Wise Coded Modulation for Four-Dimensional Hurwitz-Integer Constellations

In state-of-the-art fiber-optical systems and upcoming wireless standards, transmission over both planes of polarization of electromagnetic waves is an important approach to increase the spectral efficiency. To this end, four-dimensional modulation schemes are suited. In this paper, coded modulation for signal constellations over the Hurwitz integers, an isomorphic representation of the four-dimensional checkerboard lattice, is studied. In particular, a two-stage coding strategy is proposed where the components of the four-dimensional signal are preprocessed jointly before conventional coded-modulation techniques like bit-interleaved coded modulation or multistage decoding are applied individually per dimension. The theoretical capacities as well as numerical results from simulations with LDPC codes show that the proposed approach enables a performance gain over the straightforward application of ASK constellations per dimension or QAM constellations per polarization.