A new efficient parametric algorithm for implementing the low density lattice codes belief propagation decoder is presented. In the new algorithm the messages passed over the edges are represented by Gaussian parameters lists, and the decoding algorithm uses the low density lattice codes propagation properties in order to group lists efficiently according to anew criteria. The new algorithm attains essentially the same performance as the quantized decoder, proposed in previous work. The new algorithm advantage in comparison to previous works is its smaller storage requirements and its relatively low computational complexity. 7copy; 2009 IEEE.