Coding and modulation for the gaussian channel, in the absence or in the presence of fluctuations

Abstract

Looking for systems which combine coding and multilevel modulation whose Euclidean distance distribution is close to that which results in the average from random coding, we consider the combination of an MDS code over a large-size alphabet and a one-to-one mapping of the alphabet into a symmetric constellation e.g., phase modulation. Its performance in the presence of additive Gaussian noise can be predicted from that of random coding, provided the signal-to-noise ratio is small enough. The results exhibit the sphere hardening phenomenon whether or not amplitude fluctuations are present. Weighted demodulator output and soft decoding should be effected in order to achieve this performance. Such decoding can be done in principle according to previous works by Fang and Battail. A prohibitive complexity can be avoided only at the expense of strict optimality.