  Low density generator matrix (LDGM) codes have an acceptable performance
under iterative decoding algorithms. This idea is used to construct a class of
lattices with relatively good performance and low encoding and decoding
complexity. To construct such lattices, Construction D is applied to a set of
generator vectors of a class of LDGM codes. Bounds on the minimum distance and
the coding gain of the corresponding lattices and a corollary for the cross
sections and projections of these lattices are provided. The progressive edge
growth (PEG) algorithm is used to construct a class of binary codes to generate
the corresponding lattice. Simulation results confirm the acceptable
performance of these class of lattices.
