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dc.contributor.authorWittawat Kositwattanarerken_US
dc.identifier.citation2017 IEEE International Symposium on Information Theory (ISIT)en_US
dc.description.abstractConstructions of lattices are known to have a strong connection to the study of classical linear codes over F2; one such celebrated construction is that of Barnes-Wall (BW) lattices over Z[i], with i = √-1, wherein weighted sum of nested Reed-Muller codes over powers of the base 1 + i leads to the famous multi-level construction of BW lattices. Although these constructions facilitate simple encoding and decoding of information bits, the resulting codewords need to be mapped onto their representatives in order to reduce the average energy of the lattice code. Drawing inspirations from the case of BW lattices, in this work, we address a general question of how to arrive at representatives of the codewords of a lattice code over Ζ[θ], where θ is a quadratic integer, that is generated via a multi-level construction over linear codes over Fg, for q > 2. In particular, we introduce a novel shaping function τ: Ζ[θ] → Ζ[θ] on the components of lattice codewords, and prove that the natural constellation of lattices from multi-level constructions can be rearranged into a multi-dimensional cube or parallelepiped under such a map. We demonstrate numerically that our mapping results in a reduction of the average energy of lattice constellations. Our proposed mapping has applications in communications, particularly in encoding and decoding of lattice codes from multi-level constructions over q-ary linear codes.en_US
dc.publisherInstitute of Electrical and Electronics Engineers Inc.en_US
dc.subjectLattice codesen_US
dc.subjectMulti dimensionalen_US
dc.subjectLattice constellationen_US
dc.subjectReed-Muller codesen_US
dc.subjectForward error correctionen_US
dc.subjectInformation theoryen_US
dc.subjectSignal encodingen_US
dc.titleOn shaping complex lattice constellations from multi-level constructionsen_US
Appears in Collections:Mathematics: International Proceedings

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