  LDPC lattices were the first family of lattices that equipped with iterative
decoding algorithms under which they perform very well in high dimensions. In
this paper, we introduce quasi cyclic low density parity check (QC-LDPC)
lattices as a special case of LDPC lattices with one binary QC-LDPC code as
their underlying code. These lattices are obtained from Construction A of
lattices providing us to encode them efficiently using shift registers. To
benefit from an encoder with linear complexity in dimension of the lattice, we
obtain the generator matrix of these lattices in "quasi cyclic" form. We
provide a low-complexity decoding algorithm of QC-LDPC lattices based on sum
product algorithm. To design lattice codes, QC-LDPC lattices are combined with
nested lattice shaping that uses the Voronoi region of a sublattice for code
shaping. The shaping gain and shaping loss of our lattice codes with dimensions
$40$, $50$ and $60$ using an optimal quantizer, are presented. Consequently, we
establish a family of lattice codes that perform practically close to the
sphere bound.
