  We study some structural properties of Construction-A lattices obtained from
low density parity check (LDPC) codes over prime fields. Such lattices are
called low density Construction-A (LDA) lattices, and permit low-complexity
belief propagation decoding for transmission over Gaussian channels. It has
been shown that LDA lattices achieve the capacity of the power constrained
additive white Gaussian noise (AWGN) channel with closest lattice-point
decoding, and simulations suggested that they perform well under belief
propagation decoding. We continue this line of work, and prove that these
lattices are good for packing and mean squared error (MSE) quantization, and
that their duals are good for packing. With this, we can conclude that codes
constructed using nested LDA lattices can achieve the capacity of the power
constrained AWGN channel, the capacity of the dirty paper channel, the rates
guaranteed by the compute-and-forward protocol, and the best known rates for
bidirectional relaying with perfect secrecy.
