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Sociedade Brasileira de Telecomunicações

Modulations for Large Signal Constellations Coming from Embedding of Complete Graph


The integrated system of data transmission, encoding, modulation and block channels are projected in dependent ways with the purpose of getting an integrated action from those elements, and the elimination of additional devices with incompatibility treatment, caused by inadequate choice of some those components. In this system, the modulation and encoding projects take place in topological spaces (Ω; d), where Ω is Riemannian manifolds and d is a metric on Ω, which the discrete memoryless channel Cm, like a graph, is embedded. For each embedding Cm ,! Ω, it’s possible to determine accurately a topological modulation project on Ω, in the sense of knowing the decision regions (or Voronoi’s regions) of each constellation signal. The paper’s purpose is to identify topological projects of modulation on surfaces for large constellations, mainly the regular modulations. The procedures to obtain these projects are based on the method of the current graph developed by Gustin and Youngs and used in the proof of Color Graph Conjecture by Heawood.

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