Multilevel Constructions: Coding, Packing and Geometric Uniformity

Maiara F. Bollauf; Ram Zamir; Sueli I.R. Costa

doi:10.1109/TIT.2019.2933219

Multilevel Constructions: Coding, Packing and Geometric Uniformity

Maiara F. Bollauf, Ram Zamir, Sueli I.R. Costa

School of Electrical Engineering

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Article number	8788649
Pages (from-to)	7669-7681
Number of pages	13
Journal	IEEE Transactions on Information Theory
Volume	65
Issue number	12
DOIs	https://doi.org/10.1109/TIT.2019.2933219
State	Published - Dec 2019

Keywords

Lattice constructions
construction C∗
construction c
geometrically uniform constellation
minimum distance

All Science Journal Classification (ASJC) codes

Information Systems
Computer Science Applications
Library and Information Sciences

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10.1109/TIT.2019.2933219

Cite this

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title = "Multilevel Constructions: Coding, Packing and Geometric Uniformity",

abstract = "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.",

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year = "2019",

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doi = "10.1109/TIT.2019.2933219",

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T1 - Multilevel Constructions

T2 - Coding, Packing and Geometric Uniformity

AU - Bollauf, Maiara F.

AU - Zamir, Ram

AU - Costa, Sueli I.R.

PY - 2019/12

Y1 - 2019/12

N2 - 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.

AB - 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.

KW - Lattice constructions

KW - construction C∗

KW - construction c

KW - geometrically uniform constellation

KW - minimum distance

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U2 - 10.1109/TIT.2019.2933219

DO - 10.1109/TIT.2019.2933219

M3 - مقالة

SN - 0018-9448

VL - 65

SP - 7669

EP - 7681

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 12

M1 - 8788649

ER -

Multilevel Constructions: Coding, Packing and Geometric Uniformity

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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