Construction A of Lattices Over Number Fields and Block Fading (Wiretap) Coding

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...

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Bibliographic Details
Published in:IEEE transactions on information theory 2015-05, Vol.61 (5), p.2273-2282
Main Authors: Kositwattanarerk, Wittawat, Soon Sheng Ong, Oggier, Frederique
Format: Article
Language:English
Subjects:
Algebra
Binary system
Block codes
Fading
Generators
Information theory
Ink
Lattice theory
Lattices
Linear codes
Vectors
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Summary: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 ), 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.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2015.2416340