Graphs, tessellations, and perfect codes on flat tori

Quadrature amplitude modulation (QAM)-like signal sets are considered in this paper as coset constellations placed on regular graphs on surfaces known as flat tori. Such signal sets can be related to spherical, block, and trellis codes and may be viewed as geometrically uniform (GU) in the graph met...

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Bibliographic Details
Published in:IEEE transactions on information theory 2004-10, Vol.50 (10), p.2363-2377
Main Authors: Costa, S.I.R., Muniz, M., Agustini, E., Palazzo, R.
Format: Article
Language:English
Subjects:
Amplitude modulation
Applied sciences
Codes
Coding, codes
Constellation diagram
Convolutional codes
Euclidean distance
Euclidean space
Exact sciences and technology
Extraterrestrial measurements
Graphs
Information, signal and communications theory
Labeling
Lattices
Modulation coding
Quadrature amplitude modulation
Signal and communications theory
Signal design
Systems, networks and services of telecommunications
Telecommunications
Telecommunications and information theory
Transmission and modulation (techniques and equipments)
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Summary:Quadrature amplitude modulation (QAM)-like signal sets are considered in this paper as coset constellations placed on regular graphs on surfaces known as flat tori. Such signal sets can be related to spherical, block, and trellis codes and may be viewed as geometrically uniform (GU) in the graph metric in a sense that extends the concept introduced by Forney . Homogeneous signal sets of any order can then be labeled by a cyclic group, induced by translations on the Euclidean plane. We construct classes of perfect codes on square graphs including Lee spaces, and on hexagonal and triangular graphs, all on flat tori. Extension of this approach to higher dimensions is also considered.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2004.834754