Computationally Efficient Global Optimization of Labelling in Non-Uniform QAM Constellations

We present a computationally efficient method of optimizing the mapper (binary labelling of symbols) in the digital communication system to minimize the bit error probability. We note that high density of local minima makes this optimization problem difficult. We experiment with the simulated annealing (SA) method for this optimization problem as this method has a proven theoretical result of convergence to a global minimum. To obtain a high-quality labelling with reduced computational load, we propose a method that uses an approximated symbol error matrix (SEM), the matrix of probabilities of pairwise symbol error, for evaluating the objective function value for each labelling. Our experiments show that this approximation approach still finds relatively good solutions, which are comparable solutions attained by the SA that uses the exact SEM.