 
Summary: Pairwise Optimization of Modulation Constellations
Brendan Moore, Glen Takahara and Fady Alajaji
Dept. of Mathematics and Statistics
Queen's University
Kingston, Ontario, Canada
{brendan,takahara,fady}@mast.queensu.ca
Abstract
The design of twodimensional signal constellations
for the transmission of binary nonuniform memoryless
sources over additive white Gaussian noise channels
is investigated. The main application of this problem
is the implementation of improved constellations where
transmitted data is highly nonuniform. A simple algo
rithm, which optimizes a constellation by rearranging
its points in a pairwise fashion (i.e., two points are
modified a time with the other points remaining fixed),
is presented. In general, the optimized constellations
depend on both the source statistics and the signal
tonoise ratio (SNR) in the channel. We show that
constellations designed with source statistics considered
