The continuous demand for capacity and the limited available spectrum in wireless and wired communication has led to reliance on advanced modulation techniques to dramatically increase the number of bits per hertz per second. This demand in capacity and using the higher order constellations shorten the link range, and as a result, system gain becomes an important characteristic. The modulation techniques described here improve the system gain by, e.g., as much as 2.5 dB in high order modulations such as 4096-QAM. The modulation techniques include reducing the peak to average ratio and adding shaping gain. These techniques dramatically improve the system capacity, system gain, power consumption and system cost.