scholarly journals Rotated Z^n-Lattices via Real Subfields of Q(\zeta_2r)

2019 ◽  
Vol 20 (3) ◽  
pp. 445
Author(s):  
Antonio A. Andrade ◽  
José C. Interlando
Keyword(s):  
Cyclotomic Field ◽  
Full Diversity ◽  
Totally Real

A method for constructing rotated Z^n-lattices, with n a power of 2, based on totally real subfields of the cyclotomic field Q(\zeta_{2^r}), where r\geq 4 is an integer, is presented. Lattices exhibiting full diversity in some dimensions n not previously addressed are obtained.

scholarly journals Constructions of Dense Lattices of Full Diversity

2020 ◽  
Vol 21 (2) ◽  
pp. 299
Author(s):  
A. A. Andrade ◽  
A. J. Ferrari ◽  
J. C. Interlando ◽  
R. R. Araujo
Keyword(s):  
Real Number ◽  
Fading Channels ◽  
Packing Density ◽  
Signal Transmission ◽  
Cyclotomic Field ◽  
Sphere Packing ◽  
Number Fields ◽  
Trace Form ◽  
Full Diversity ◽  
Totally Real

A lattice construction using Z-submodules of rings of integers of number fields is presented. The construction yields rotated versions of the laminated lattices A_n for n = 2,3,4,5,6, which are the densest lattices in their respective dimensions. The sphere packing density of a lattice is a function of its packing radius, which in turn can be directly calculated from the minimum squared Euclidean norm of the lattice. Norms in a lattice that is realized by a totally real number field can be calculated by the trace form of the field restricted to its ring of integers. Thus, in the present work, we also present the trace form of the maximal real subfield of a cyclotomic field. Our focus is on totally real number fields since their associated lattices have full diversity. Along with high packing density, the full diversity feature is desirable in lattices that are used for signal transmission over both Gaussian and Rayleigh fading channels.

scholarly journals A Construction of Rotated Lattices via Totally Real Subfields of the Cyclotomic Field Q(z_p)

2019 ◽  
Vol 20 (3) ◽  
pp. 561
Author(s):  
Antonio A. Andrade ◽  
Everton L. Oliveira ◽  
José C. Interlando
Keyword(s):  
Fading Channel ◽  
Rayleigh Fading ◽  
Cyclotomic Field ◽  
Number Fields ◽  
Rayleigh Fading Channel ◽  
Ring Of Integers ◽  
Full Diversity ◽  
Alternative Approach ◽  
Totally Real ◽  
Modulation Diversity

The theory of lattices have shown to be useful in information theory and rotated lattices with high modulations diversity have been extensively studied as an alternative approach for transmission over a Rayleigh-fading channel, where the performance of this modulation schemes essentially depends of the modulation diversity and of the minimum product distance to achieve substantial coding gains. The maximum diversity of a rotated lattice is guaranteed when we use totally real number fields and the minimum product distance is optimized by considering fields with minimum discriminant. In this paper, we present a construction of rotated lattice for the Rayleigh fading channel in Euclidean spaces with full diversity, where this construction is through a totally real subfield K of the cyclotomic field Q(z_p), where p is an odd prime, obtained by endowing their ring of integers.

Constructions of rotated lattice constellations in dimensions power of 3

2018 ◽  
Vol 17 (09) ◽  
pp. 1850175 ◽  
Author(s):  
Agnaldo José Ferrari ◽  
Antonio Aparecido de Andrade
Keyword(s):  
Positive Integer ◽  
Real Number ◽  
Fading Channels ◽  
Lower Bounds ◽  
Rayleigh Fading ◽  
Signal Transmission ◽  
Number Fields ◽  
Rayleigh Fading Channels ◽  
Full Diversity ◽  
Totally Real

In this paper, we present the constructions of rotated [Formula: see text]-lattices, where [Formula: see text] is a positive integer, via [Formula: see text]-modules of the ring of the integers [Formula: see text]. Our focus is on totally real number fields since the associated lattices have full diversity and then may be suitable for signal transmission over both Gaussian and Rayleigh fading channels. Lower bounds for the minimum product distances of such construction are also presented.

scholarly journals Monogenity of totally real algebraic extension fields over a cyclotomic field

2016 ◽  
Vol 158 ◽  
pp. 348-355 ◽  
Author(s):  
Nadia Khan ◽  
Shin-ichi Katayama ◽  
Toru Nakahara ◽  
Tsuyoshi Uehara
Keyword(s):  
Cyclotomic Field ◽  
Algebraic Extension ◽  
Totally Real

Algebraic constructions of rotated unimodular lattices and direct sum of Barnes–Wall lattices

2020 ◽  
pp. 2150029
Author(s):  
João Eloir Strapasson ◽  
Agnaldo José Ferrari ◽  
Grasiele Cristiane Jorge ◽  
Sueli Irene Rodrigues Costa
Keyword(s):  
Real Number ◽  
Fading Channels ◽  
Rayleigh Fading ◽  
Signal Transmission ◽  
Number Fields ◽  
Rayleigh Fading Channels ◽  
Direct Sum ◽  
Full Diversity ◽  
Algebraic Constructions ◽  
Totally Real

In this paper, we construct some families of rotated unimodular lattices and rotated direct sum of Barnes–Wall lattices [Formula: see text] for [Formula: see text] and [Formula: see text] via ideals of the ring of the integers [Formula: see text] for [Formula: see text] and [Formula: see text]. We also construct rotated [Formula: see text] and [Formula: see text]-lattices via [Formula: see text]-submodules of [Formula: see text]. Our focus is on totally real number fields since the associated lattices have full diversity and then may be suitable for signal transmission over both Gaussian and Rayleigh fading channels. The minimum product distances of such constructions are also presented here.

REPRESENTING Ω(l∞) FOR REAL ABELIAN FIELDS

2003 ◽  
Vol 02 (03) ◽  
pp. 237-276 ◽  
Author(s):  
JÜRGEN RITTER ◽  
ALFRED WEISS
Keyword(s):  
Real Number ◽  
Prime Number ◽  
Cyclotomic Field ◽  
Number Fields ◽  
Iwasawa Theory ◽  
Root Number ◽  
Abelian Extensions ◽  
Main Conjecture ◽  
Abelian Fields ◽  
Totally Real

For real subfields K of a cyclotomic field ℚ(ς) we remove the tameness assumption at a given odd prime number l, which was needed in [11] in order to establish the equivalence of the Lifted Root Number Conjecture at l and an equivariant main conjecture of Iwasawa theory for abelian extensions of totally real number fields K/k.

Single Symbol Decodable QO-STBC with Full Diversity

2014 ◽  
Vol E97.A (1) ◽  
pp. 2-6
Author(s):  
Naotoshi YODA ◽  
Chang-Jun AHN ◽  
Ken-ya HASHIMOTO
Keyword(s):  
Full Diversity

Curvature inequalities for C-totally real doubly warped products of locally conformal almost cosymplectic manifolds

Filomat ◽  
2017 ◽  
Vol 31 (20) ◽  
pp. 6449-6459 ◽  
Author(s):  
Akram Ali ◽  
Siraj Uddin ◽  
Wan Othman ◽  
Cenap Ozel
Keyword(s):  
Sectional Curvature ◽  
Mean Curvature ◽  
Warped Product ◽  
Warped Products ◽  
Equality Case ◽  
Cosymplectic Manifolds ◽  
Almost Cosymplectic Manifold ◽  
Locally Conformal ◽  
Totally Real ◽  
Optimal Inequalities

In this paper, we establish some optimal inequalities for the squared mean curvature in terms warping functions of a C-totally real doubly warped product submanifold of a locally conformal almost cosymplectic manifold with a pointwise ?-sectional curvature c. The equality case in the statement of inequalities is also considered. Moreover, some applications of obtained results are derived.

Women’s Participation in the Public Domain Under Human Rights Law: Towards a Participatory Equality Paradigm Shift

2018 ◽  
Author(s):  
Ruth Rubio-Marín
Keyword(s):  
Human Rights ◽  
Gender Quotas ◽  
Political Rights ◽  
Human Rights Law ◽  
Private Governance ◽  
Public And Private ◽  
Full Diversity ◽  
Women's Participation ◽  
Indigenous Groups ◽  
Participation Of Women

This chapter explores how human rights law has contributed to the shift towards participatory gender equality by legitimating the adoption of quotas and parity mechanisms to ensure women’s equal participation in decision-making. Since the adoption of CEDAW, human rights law has moved away from formal equality notions that simply affirm women’s equal political rights. Instead, we see growing endorsement of substantive equality doctrines that validate the adoption of gender quotas, initially as temporary special measures to ensure women equal opportunities, and, more recently, as permanent measures targeting the gender-balanced composition of an ever-expanding range of public and private governance bodies. The chapter explores how human rights law connects this participatory turn to issues of pluralism, calling attention to the need for public bodies to represent the full diversity of the population, and calling on state parties to increase the participation of women from ethnic minorities, indigenous groups, and religious minorities.

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