On the optimal discrete bit loading for multicarrier systems with constraints

In this paper optimal discrete bit loading algorithms for multicarrier systems employing DMT (discrete multitone) are proposed. The solutions are derived under the additional constraints on either the maximum allowable energy for each subchannel or the maximum cardinality of the QAM constellations that are used. The optimal loading is proved to be a greedy algorithm which employs a bit-removal procedure. In many practical cases it is more effective from a computational point of view in comparison with the corresponding optimal greedy algorithm employing bit-filling. Conditions for the optimality of a greedy approach (in general suboptimal) in this context are also provided. The solutions are developed in the framework of matroid theory, resorting to some results concerning combinatorial optimization.