Doping of Extended Mappings for Signal Shaping

The adaption of symbol probabilities to the Maxwell-Boltzman distribution enables a shaping gain of up to 1.53 dB over uniform distributions. We assign a variable number of labels to each signal point to implement signal shaping. The ambiguous mapping requires a larger label alphabet that we obtain by increasing the label length. The ambiguous mappings enable an additional coding gain due to the increased label length which allows the use of a lower coding rate. We deduce the optimum MAP detector and approximate the optimum Maxwell-Boltzman distribution by a rounding based algorithm. Some optimized label distributions and extended mappings are given for 16- and 64-QAM. Extended mappings for signal shaping combine the advantages of a more powerful channel code and the increase in channel capacity. Simulation results promise a very low bit error floor with extremely simple channel codes.