Superposition coding for power- and bandwidth efficient communication over the Gaussian channel

A method for power- and bandwidth efficient communication over the Gaussian channel is presented. The method is based on the superposition of binary random variables. As an example we design a signal constellation for a spectral efficiency of 10 bit/s/Hz. The constellation has a constrained capacity limit only 0.18 dB from the Gaussian capacity limit. Moreover, we show that combined with multi-level coding and low-density parity-check codes, a low bit-error rate is achieved at 0.6 dB from the Gaussian capacity limit for a large codeword length.