  The non-ergodic fading channel is a useful model for various wireless
communication channels in both indoor and outdoor environments. Building on
Poltyrev's work on infinite lattice constellations for the Gaussian channel, we
derive a Poltyrev outage limit (POL) for lattices in presence of block fading.
We prove that the diversity order of this POL is equal to the number of degrees
of freedom in the channel. Further, we describe full-diversity constructions of
real lattices defined by their integer-check matrix, i.e., the inverse of their
generator matrix. In the first construction suited to maximum-likelihood
decoding, these lattices are defined by sparse (low-density) or non-sparse
integer-check matrices. Based on a special structure of the lattice binary
image, a second full-diversity lattice construction is described for sparse
integer-check matrices in the context of iterative probabilistic decoding. Full
diversity is theoretically proved in both cases. We also propose a method to
construct lattices for diversity order 4 suitable for iterative probabilistic
decoding. Computer simulation results for diversity order L = 2 and L = 4
confirm that the proposed low-density lattices attain the maximal diversity
order. The newly defined POL is used during this simulation to declare an
outage error without decoding, which drastically improves the decoding runtime.
