  In this paper, we propose a new approach to proving results regarding channel
coding schemes based on construction-A lattices for the Additive White Gaussian
Noise (AWGN) channel that yields new characterizations of the code construction
parameters, i.e., the primes and dimensions of the codes, as functions of the
block-length. The approach we take introduces an averaging argument that
explicitly involves the considered parameters. This averaging argument is
applied to a generalized Loeliger ensemble to provide a more practical proof of
the existence of AWGN-good lattices, and to characterize suitable parameters
for the lattice Gaussian coding scheme proposed by Ling and Belfiore.
