Antonio C. de A. Campello

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In this paper we study sequences of lattices which are, up to similarity, projections of Z onto hyperplanes v⊥, with v ∈ Z. We show a sufficient condition to construct sequences converging at rate O(1/ ‖v‖) to integer lattices and exhibit explicit constructions for some important families of lattices. The problem addressed here arises from a question of(More)
We investigate perfect codes in Zn in the `p metric. Upper bounds for the packing radius r of a linear perfect code in terms of the metric parameter p and the dimension n are derived. For p = 2 and n = 2, 3, we determine all radii for which there exist linear perfect codes. The non-existence results for codes in Zn presented here imply non-existence results(More)
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(More)
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(More)
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(More)
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(More)
In this paper we consider the problem of transmitting a continuous alphabet discrete-time source over an AWGN channel. The design of good curves for this purpose relies on geometrical properties of spherical codes and projections of N-dimensional lattices. We propose a constructive scheme based on a set of curves on the surface of a 2N-dimensional sphere(More)
Some hard problems from lattices, like LWE (Learning with Errors), are particularly suitable for application in Cryptography due to the possibility of using worst-case to average-case reductions as evidence of strong security properties. In this work, we show two LWE-based constructions of zero-knowledge identification schemes and discuss their performance(More)
We consider the probability of data loss in an erasure coded distributed storage system. Data loss in an erasure coded system depends on the repair duration and the failure probability of individual disks. This dependence on the repair duration complicates the data loss probability analysis. In previous work, the data loss probability of such systems has(More)
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(More)