Multilevel Constructions: Coding, Packing and Geometric Uniformity

Multilevel Constructions: Coding, Packing and Geometric Uniformity

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 propertie...

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Veröffentlicht in:IEEE transactions on information theory 2019-12, Vol.65 (12), p.7669-7681
Hauptverfasser: Bollauf, Maiara F., Zamir, Ram, Costa, Sueli I. R.
Format: Artikel
Sprache:eng
Schlagworte:
Binary codes
Codes
Constellation diagram
Constellations
construction <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">C
construction c
Decoding
geometrically uniform constellation
Labeling
Lattice constructions
Lattices
Linear codes
minimum distance
Multilevel
Vector quantization
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Zusammenfassung: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^\star . We investigate the geometric uniformity, latticeness, and minimum distance properties of Construction C^\star , and discuss its superior packing efficiency when compared to Construction C.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2019.2933219