Construction a of lattices over number fields and block fading (wiretap) coding

Wittawat Kositwattanarerk; Soon Sheng Ong; Frédérique Oggier

doi:10.1109/TIT.2015.2416340

Construction a of lattices over number fields and block fading (wiretap) coding

Wittawat Kositwattanarerk
, Soon Sheng Ong
, Frédérique Oggier

Mahidol University
Nanyang Technological University
Raffles Institution

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

28 Citations (Scopus)

Abstract

We propose a lattice construction from totally real and complex multiplication fields, which naturally generalizes Construction A of lattices from p -ary codes obtained from the cyclotomic field Q(ζ_p), p a prime, which in turn contains the so-called Construction A of lattices from binary codes as a particular case. We focus on the maximal totally real subfield Q(ζ_p^-r)+ζ_p^-r) of the cyclotomic field Q(ζ_p^r), ≥ 1. Our construction has applications to coset encoding of algebraic lattice codes for block fading channels, and in particular for block fading wiretap channels.

Original language	English
Pages (from-to)	2273-2282
Number of pages	10
Journal	IEEE Transactions on Information Theory
Volume	61
Issue number	5
DOIs	https://doi.org/10.1109/TIT.2015.2416340
Publication status	Published - 1 May 2015
Externally published	Yes

Keywords

Construction A
coset codes
lattice codes
number fields

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10.1109/TIT.2015.2416340

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title = "Construction a of lattices over number fields and block fading (wiretap) coding",

abstract = "We propose a lattice construction from totally real and complex multiplication fields, which naturally generalizes Construction A of lattices from p -ary codes obtained from the cyclotomic field Q(ζp), p a prime, which in turn contains the so-called Construction A of lattices from binary codes as a particular case. We focus on the maximal totally real subfield Q(ζp-r)+ζp-r) of the cyclotomic field Q(ζpr), ≥ 1. Our construction has applications to coset encoding of algebraic lattice codes for block fading channels, and in particular for block fading wiretap channels.",

keywords = "Construction A, coset codes, lattice codes, number fields",

author = "Wittawat Kositwattanarerk and Ong, \{Soon Sheng\} and Fr{\'e}d{\'e}rique Oggier",

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

year = "2015",

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doi = "10.1109/TIT.2015.2416340",

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T1 - Construction a of lattices over number fields and block fading (wiretap) coding

AU - Kositwattanarerk, Wittawat

AU - Ong, Soon Sheng

AU - Oggier, Frédérique

PY - 2015/5/1

Y1 - 2015/5/1

N2 - We propose a lattice construction from totally real and complex multiplication fields, which naturally generalizes Construction A of lattices from p -ary codes obtained from the cyclotomic field Q(ζp), p a prime, which in turn contains the so-called Construction A of lattices from binary codes as a particular case. We focus on the maximal totally real subfield Q(ζp-r)+ζp-r) of the cyclotomic field Q(ζpr), ≥ 1. Our construction has applications to coset encoding of algebraic lattice codes for block fading channels, and in particular for block fading wiretap channels.

AB - We propose a lattice construction from totally real and complex multiplication fields, which naturally generalizes Construction A of lattices from p -ary codes obtained from the cyclotomic field Q(ζp), p a prime, which in turn contains the so-called Construction A of lattices from binary codes as a particular case. We focus on the maximal totally real subfield Q(ζp-r)+ζp-r) of the cyclotomic field Q(ζpr), ≥ 1. Our construction has applications to coset encoding of algebraic lattice codes for block fading channels, and in particular for block fading wiretap channels.

KW - Construction A

KW - coset codes

KW - lattice codes

KW - number fields

UR - https://www.scopus.com/pages/publications/84928542128

U2 - 10.1109/TIT.2015.2416340

DO - 10.1109/TIT.2015.2416340

M3 - Article

AN - SCOPUS:84928542128

SN - 0018-9448

VL - 61

SP - 2273

EP - 2282

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 5

ER -

Construction a of lattices over number fields and block fading (wiretap) coding

Abstract

Keywords

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