  A lattice decoder which represents messages explicitly as a mixture of
Gaussians functions is given. In order to prevent the number of functions in a
mixture from growing as the decoder iterations progress, a method for replacing
N Gaussian functions with M Gaussian functions, with M < N, is given. A squared
distance metric is used to select functions for combining. A pair of selected
Gaussians is replaced by a single Gaussian with the same first and second
moments. The metric can be computed efficiently, and at the same time, the
proposed algorithm empirically gives good results, for example, a dimension 100
lattice has a loss of 0.2 dB in signal-to-noise ratio at a probability of
symbol error of 10^{-5}.
