Multidimensional Lattices and Limit Efficiency of Modulation and Coding

For the Gaussian channel we investigate how the exponent of the additive estimate for the mean coding error probability over the ensemble of codes (the computational rate) $R_0$ depends on the signal-to-noise ratio per sample provided that the input symbols for the channel are chosen from a subset of a multidimensional lattice. The asymptotic behavior of $R_0$ is considered with respect to the S/N per sample, the alphabet's cardinality, and the number of samples. Some numerical results are presented and some examples are discussed.