A Condition for Optimality of Two-Dimensional Signal Constellations

1985 ◽  
Vol 33 (11) ◽  
pp. 1220-1222 ◽  
Author(s):  
S. Sayegh
Keyword(s):  
Two Dimensional ◽  
Signal Constellations

scholarly journals On the structure of multipliers ofℤ2

2003 ◽  
Vol 2003 (15) ◽  
pp. 935-946
Author(s):  
Edgar Martínez-Moro ◽  
Roberto Canogar-Mckenzie
Keyword(s):  
Association Scheme ◽  
Coding Theory ◽  
Combinatorial Structure ◽  
Two Dimensional ◽  
Gaussian Integer ◽  
Main Application ◽  
Mannheim Metric ◽  
Signal Constellations

We show the combinatorial structure ofℤ2modulo sublattices similar toℤ2. The tool we use for dealing with this purpose is the notion of association scheme. We classify when the scheme defined by the lattice is imprimitive and characterize its decomposition in terms of the decomposition of the Gaussian integer defining the lattice. This arises in the classification of different forms of tilingℤ2by lattices of this type. The main application of these structures is that they are closely related to two-dimensional signal constellations with a Mannheim metric in the coding theory.

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