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

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

6 Scopus citations

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

Funding

Funders	Funder number
Fundação de Amparo à Pesquisa do Estado de São Paulo	2013/25977-7
Conselho Nacional de Desenvolvimento Científico e Tecnológico	313326/2017-7, 140797/2017-3 Grant 312926/2013-8
Israel Science Foundation	676/15

Keywords

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

Access to Document

10.1109/TIT.2019.2933219

Cite this

@article{b1b01ff66e4f4fe49649c9b7fd894630,

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.",

keywords = "Lattice constructions, construction C∗, construction c, geometrically uniform constellation, minimum distance",

author = "Bollauf, {Maiara F.} and Ram Zamir and Costa, {Sueli I.R.}",

note = "Publisher Copyright: {\textcopyright} 1963-2012 IEEE.",

year = "2019",

month = dec,

doi = "10.1109/TIT.2019.2933219",

language = "אנגלית",

volume = "65",

pages = "7669--7681",

journal = "IEEE Transactions on Information Theory",

issn = "0018-9448",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

number = "12",

}

TY - JOUR

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

UR - http://www.scopus.com/inward/record.url?scp=85077436367&partnerID=8YFLogxK

U2 - 10.1109/TIT.2019.2933219

DO - 10.1109/TIT.2019.2933219

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85077436367

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

Funding

Keywords

Access to Document

Other files and links

Fingerprint

Cite this