Lattice and special nonlattice multilevel constellations constructed from binary codes, such as Constructions A, C, and D, have relevant applications in Mathematics (sphere packing) and in Communication (multi-stage decoding and efficient vector quantization). In this work, we explore some properties of Construction C, in particular its geometric uniformity. We then propose a new multilevel construction, inspired by bit interleaved coded modulation (BICM), that we call Construction C∗. We investigate the geometric uniformity, latticeness, and minimum distance properties of Construction C∗ , and discuss its superior packing efficiency when compared to Construction C.
- Lattice constructions
- construction C∗
- construction c
- geometrically uniform constellation
- minimum distance