A genetic algorithm for designing constellations with low error floors

The error floor of bit-interleaved coded modulation with iterative decoding (BICM-ID) can be minimized for a particular constellation by maximizing the harmonic mean of the squared-Euclidian distances of signals whose labels differ in just one bit position. This problem has been formulated as an instance of the Quadratic Assignment Problem (QAP) and solved using the Reactive Tabu Search (RTS). In this paper, we propose a genetic algorithm for solving the symbol labeling problem and show that it usually yields designs that are isomorphic to those obtained using RTS. We then extend the algorithm to optimize not only the labelings of the signal points, but also their location in the signal space. Using this approach, new constellations of cardinality 16, 32, and 64 are evolved that have an error floor lower than that of QAM or PSK modulation. The new constellations exhibit gains of 1.32 and 0.88 dB over the best 16-QAM and 64-QAM constellations reported previously.