Abstract
Signal constellations having lattice structure have been studied as meaningful means for signal transmission over Gaussian channel. Usually the problem of finding good signal constellations for a Gaussian channel is associated with the search for lattices with high packing density, where in general the packing density is usually hard to estimate. The aim of this paper was to illustrate the fact that the polynomial ring \(\mathbb {Z}[x]\) can produce lattices with maximum achievable center density, where \(\mathbb {Z}\) is the ring of rational integers. Essentially, the method consists of constructing a generator matrix from a quotient ring of \(\mathbb {Z}[x]\).
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Acknowledgements
The authors would like to thank the anonymous reviewers for their insightful comments that greatly improved the quality of this work. This work was partially supported by Fapesp 2013/25977-7 and 2014/14449-2, and CNPq 429346/2018-2.
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Communicated by Thomas Aaron Gulliver.
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Ferrari, A.J., de Andrade, A.A. Algebraic lattices via polynomial rings. Comp. Appl. Math. 38, 163 (2019). https://doi.org/10.1007/s40314-019-0948-8
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DOI: https://doi.org/10.1007/s40314-019-0948-8