Lattice constellations and codes from quadratic number fields

We propose new classes of linear codes over integer rings of quadratic extensions of Q, the field of rational numbers. The codes are considered with respect to a Mannheim metric, which is a Manhattan metric modulo a two-dimensional (2-D) grid. In particular, codes over Gaussian integers and Eisenstein-Jacobi integers are extensively studied. Decoding algorithms are proposed for these codes when up to two coordinates of a transmitted code vector are affected by errors of arbitrary Mannheim weight. Moreover, we show that the proposed codes are maximum-distance separable (MDS), with respect to the Hamming distance. The practical interest in such Mannheim-metric codes is their use in coded modulation schemes based on quadrature amplitude modulation (QAM)-type constellations, for which neither the Hamming nor the Lee metric is appropriate.

A low-complexity lattice-based low-PAR transmission scheme for DSL channels

This paper presents a new low-complexity multicarrier modulation (MCM) technique based on lattices which achieves a peak-to-average power ratio (PAR) as low as three. The scheme can be viewed as a drop in replacement for the discrete multitone (DMT) modulation of an asymmetric digital subscriber line modem. We show that the lattice-MCM retains many of the attractive features of sinusoidal-MCM, and does so with lower implementation complexity, O(N), compared with DMT, which requires O(N log N) operations. We also present techniques for narrowband interference rejection and power profiling. Simulation studies confirm that performance of the lattice-MCM is superior, even compared with recent techniques for PAR reduction in DMT.

A new joint coding and modulation scheme for channels with clipping

A major limitation in any high-performance digital communication system is the linearity region of the transmitting amplifier. Nonlinearities typically lead to signal clipping. Efficient communication in such conditions requires maintaining a low peak-to-average power ratio (PAR) in the transmitted signal while achieving a high throughput of data. Excessive PAR leads either to frequent clipping or to inadequate resolution in the analog-to-digital or digital-to-analog converters. Currently proposed signaling schemes for future generation wireless communications suffer from a high PAR. This paper presents a new signaling scheme for channels with clipping which achieves a PAR as low as 3. For a given linear range in the transmitter's digital-to-analog converter, this scheme achieves a lower bit-error rate than existing multicarrier schemes, owing to increased separation between constellation points. We present the theoretical basis for this new scheme, approximations for the expected bit-error rate, and simulation results. (C) 2002 Elsevier Science (USA).

Effects of cross sections tables generation and optimization on rod ejection transient analyses

Best estimate analysis of rod ejection transients requires 3D kinetics core simulators. If they use cross sections libraries compiled in multidimensional tables,interpolation errors – originated when the core simulator computes the cross sections from the table values – are a source of uncertainty in k-effective calculations that should be accounted for. Those errors depend on the grid covering the domain of state variables and can be easily reduced, in contrast with other sources of uncertainties such as the ones due to nuclear data, by choosing an optimized grid distribution. The present paper assesses the impact of the grid structure on a PWR rod ejection transient analysis using the coupled neutron-kinetics/thermal-hydraulicsCOBAYA3/COBRA-TF system. Forthispurpose, the OECD/NEA PWR MOX/UO2 core transient benchmark has been chosen, as material compositions and geometries are available, allowing the use of lattice codes to generate libraries with different grid structures. Since a complete nodal cross-section library is also provided as part of the benchmark specifications, the effects of the library generation on transient behavior are also analyzed.Results showed large discrepancies when using the benchmark library and own-generated libraries when compared with benchmark participants’ solutions. The origin of the discrepancies was found to lie in the nodal cross sections provided in the benchmark.

Low-complexity low-PAR transmission for MIMO-DSL

This letter considers clip-limited transmission over multiple-input multiple-output digital subscriber lines (MIMO-DSL). We show that a recent low complexity, low peak-to-average-ratio (PAR) single-input modulation technique can be applied to the case of multiple cross-talking channels in a bonded-DSL system. Unfortunately however the direct initialization procedure is computationally infeasible. In this paper, we provide a novel low-complexity initialization procedure. Simulations confirm that the proposed approach has superior performance in clip-limited conditions, compared with both discrete matrix multitone and vectored discrete multitone.

Error-correcting codes on a Bethe-like lattice

We analyse Gallager codes by employing a simple mean-field approximation that distorts the model geometry and preserves important interactions between sites. The method naturally recovers the probability propagation decoding algorithm as a minimization of a proper free-energy. We find a thermodynamical phase transition that coincides with information theoretical upper-bounds and explain the practical code performance in terms of the free-energy landscape.

Construction and performance of network codes

El principal objectiu d'aquest treball és implementar i exposar una descripció teòrica per a diferents esquemes de Physical Layer Network Coding. Utilitzant un esquema bàsic com a punt de partida, el projecte presenta la construcció i l'anàlisis de diferents esquemes de comunicació on la complexitat va augmentant a mesura que anem avançant en el projecte. El treball està estructurat en diferents parts: primer, es presenta una introducció a Physical Layer Network Coding i a Lattice Network Codes. A continuació, s'introdueixen les eines matemàtiques necessàries per entendre el CF System. Després, s'analitza i implementa el primer esquema bàsic. A partir del qual, implementem una versió vectorial del CF System i una versió codificada amb un Hamming q-ari. Finalment, s'estudien i implementen diferents estratègies per millorar la matriu de coeficients A.

Space–Time Block Codes and the Complexity of Sphere Decoding

In wireless communications the transmitted signals may be affected by noise. The receiver must decode the received message, which can be mathematically modelled as a search for the closest lattice point to a given vector. This problem is known to be NP-hard in general, but for communications applications there exist algorithms that, for a certain range of system parameters, offer polynomial expected complexity. The purpose of the thesis is to study the sphere decoding algorithm introduced in the article On Maximum-Likelihood Detection and the Search for the Closest Lattice Point, which was published by M.O. Damen, H. El Gamal and G. Caire in 2003. We concentrate especially on its computational complexity when used in space–time coding. Computer simulations are used to study how different system parameters affect the computational complexity of the algorithm. The aim is to find ways to improve the algorithm from the complexity point of view. The main contribution of the thesis is the construction of two new modifications to the sphere decoding algorithm, which are shown to perform faster than the original algorithm within a range of system parameters.

On the construction of perfect codes from HEX signal constellations

Recently, minimum and non-minimum delay perfect codes were proposed for any channel of dimension n. Their construction appears in the literature as a subset of cyclic division algebras over Q(zeta(3)) only for the dimension n = 2(s)n(1), where s is an element of {0,1}, n(1) is odd and the signal constellations are isomorphic to Z[zeta(3)](n) In this work, we propose an innovative methodology to extend the construction of minimum and non-minimum delay perfect codes as a subset of cyclic division algebras over Q(zeta(3)), where the signal constellations are isomorphic to the hexagonal A(2)(n)-rotated lattice, for any channel of any dimension n such that gcd(n,3) = 1. (C) 2012 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

Construction of perfect space-time codes

In this work, we propose an innovative methodology to extend the construction of minimum and non-minimum delay perfect codes as a subset of cyclic division algebras over ℚ(ζ3), where the signal constellations are isomorphic to the hexagonal An 2 -rotated lattice, for any channel of any dimension n such that gcd{n, 3) = 1.

A formalized optimum code search for q-ary trellis codes

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Reaction-diffusion stochastic lattice model for a predator-prey system

We have the purpose of analyzing the effect of explicit diffusion processes in a predator-prey stochastic lattice model. More precisely we wish to investigate the possible effects due to diffusion upon the thresholds of coexistence of species, i. e., the possible changes in the transition between the active state and the absorbing state devoid of predators. To accomplish this task we have performed time dependent simulations and dynamic mean-field approximations. Our results indicate that the diffusive process can enhance the species coexistence.

Aging and fluctuation-dissipation ratio in a nonequilibrium q-state lattice model

A generalized version of the nonequilibrium linear Glauber model with q states in d dimensions is introduced and analyzed. The model is fully symmetric, its dynamics being invariant under all permutations of the q states. Exact expressions for the two-time autocorrelation and response functions on a d-dimensional lattice are obtained. In the stationary regime, the fluctuation-dissipation theorem holds, while in the transient the aging is observed with the fluctuation-dissipation ratio leading to the value predicted for the linear Glauber model.

Phase diagram of a model for a binary mixture of nematic molecules on a Bethe lattice

We investigate the phase diagram of a discrete version of the Maier-Saupe model with the inclusion of additional degrees of freedom to mimic a distribution of rodlike and disklike molecules. Solutions of this problem on a Bethe lattice come from the analysis of the fixed points of a set of nonlinear recursion relations. Besides the fixed points associated with isotropic and uniaxial nematic structures, there is also a fixed point associated with a biaxial nematic structure. Due to the existence of large overlaps of the stability regions, we resorted to a scheme to calculate the free energy of these structures deep in the interior of a large Cayley tree. Both thermodynamic and dynamic-stability analyses rule out the presence of a biaxial phase, in qualitative agreement with previous mean-field results.

Critical behavior of the susceptible-infected-recovered model on a square lattice

By means of numerical simulations and epidemic analysis, the transition point of the stochastic asynchronous susceptible-infected-recovered model on a square lattice is found to be c(0)=0.176 500 5(10), where c is the probability a chosen infected site spontaneously recovers rather than tries to infect one neighbor. This point corresponds to an infection/recovery rate of lambda(c)=(1-c(0))/c(0)=4.665 71(3) and a net transmissibility of (1-c(0))/(1+3c(0))=0.538 410(2), which falls between the rigorous bounds of the site and bond thresholds. The critical behavior of the model is consistent with the two-dimensional percolation universality class, but local growth probabilities differ from those of dynamic percolation cluster growth, as is demonstrated explicitly.