Multilevel constructions: coding, packing and geometric uniformity
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Lattice and special nonlattice multilevel constellations constructed from binary codes, such as Construction C, have relevant applications in mathematics (sphere packing) and communication problems (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, motivated by bit interleaved coded modulation, that we call Construction C^. We explore the geometric uniformity and minimum distance properties of Construction C^, and discuss its potential superior packing efficiency with respect to Construction C.
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