Antonio Campello

Algebraic lattice codes achieve the capacity of the compound block-fading channel

We propose a lattice coding scheme that achieves the capacity of the compound block-fading channel. Our lattice construction exploits the multiplicative structure of number fields and their group of units to absorb ill-conditioned channel realizations. To shape the constellation, a discrete Gaussian distribution over the lattice points is applied. A by-product of our results is a refined analysis of the probability of error of the lattice Gaussian distribution in the AWGN channel.

Algebraic lattices achieving the capacity of the ergodic fading channel

In this work we show that algebraic lattices constructed from error-correcting codes achieve the ergodic capacity of the fading channel. The main ingredients for our construction are a generalized version of the Minkowski-Hlawka theorem and shaping techniques based on the lattice Gaussian distribution. The structure of the ring of integers in a number field plays an important role in the proposed construction. In the case of independent and identically distributed fadings, the lattices considered exhibit full diversity and an exponential decay of the probability of error with respect to the blocklength.

Prediction of dopant atom distribution on nanocrystals using thermodynamic arguments

A theoretical approach aiming at the prediction of segregation of dopant atoms on nanocrystalline systems is discussed here. It considers the free energy minimization argument in order to provide the most likely dopant distribution as a function of the total doping level. For this, it requires as input (i) a fixed polyhedral geometry with defined facets, and (ii) a set of functions that describe the surface energy as a function of dopant content for different crystallographic planes. Two Sb-doped SnO2 nanocrystalline systems with different morphology and dopant content were selected as a case study, and the calculation of the dopant distributions expected for them is presented in detail. The obtained results were compared to previously reported characterization of this system by a combination of HRTEM and surface energy calculations, and both methods are shown to be equivalent. Considering its application pre-requisites, the present theoretical approach can provide a first estimation of doping atom distribution for a wide range of nanocrystalline systems. We expect that its use will support the reduction of experimental effort for the characterization of doped nanocrystals, and also provide a solution to the characterization of systems where even state-of-art analytical techniques are limited.

Flat tori, lattices and spherical codes

The foliation of a sphere in an even number of dimensions by flat tori can be used to construct discrete spherical codes and also homogeneous curves for transmitting a continuous alphabet source over an AWGN channel. In both cases the performance of the code is related to the packing density of specific lattices and their orthogonal sublattices. In the continuous case the packing density of curves relies also on the search for projection lattices with good packing density. We present here a survey of this topic including some recent research results and perspectives.

Decoding q-ary lattices in the Lee metric

Q-ary lattices can be obtained from q-ary codes using the so-called Construction A. We investigate these lattices in the Lee metric and show how their decoding process can be related to the associated codes. For prime q we derive a Lee sphere decoding algorithm for q-ary lattices, present a brief discussion on its complexity and some comparisons with the classic sphere decoding.

Codes and lattices in the l p metric

Codes and associated lattices are studied in the l_p metric, particularly in the l₁ (Lee) and the l_∞ (maximum) distances. Discussions and results on decoding processes, classification and analysis of perfect or dense codes in these metrics are presented.

Curves on Flat Tori and Analog Source-Channel Codes

In this paper, we consider the problem of transmitting a continuous alphabet discrete-time source over an additive white Gaussian noise channel in the bandwidth expansion case. We propose a constructive scheme based on a set of curves on the surface of a 2N-dimensional sphere. Our approach shows that the design of good codes for this communication problem relies on geometrical properties of spherical codes and projections of N-dimensional rectangular lattices. Theoretical comparisons with some previous works in terms of the mean squared error as a function of the channel SNR, as well as simulations, are provided.

On sequences of projections of the cubic lattice

In this paper we study sequences of lattices which are, up to similarity, projections of

Reliability of erasure coded storage systems: A geometric approach

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