  Low density parity check (LDPC) lattices are obtained from Construction D'
and a family of nested binary LDPC codes. We consider an special case of these
lattices with one binary LDPC code as underlying code. This special case of
LDPC lattices can be obtained by lifting binary LDPC codes using Construction A
lattices. The LDPC lattices were the first family of lattices which have
efficient decoding in high dimensions. We employ the encoding and decoding of
the LDPC lattices in a cooperative transmission framework. We establish two
efficient shaping methods based on hypercube shaping and Voronoi shaping, to
obtain LDPC lattice codes. Then, we propose the implementation of block Markov
encoding for one-way and two-way relay networks using LDPC lattice codes. This
entails owning an efficient method for decomposing full-rate codebook into
lower rate codebooks. We apply different decomposition schemes for one-way and
two-way relay channels which are the altered versions of the decomposition
methods of low density lattice codes (LDLCs). Due to the lower complexity of
the decoding for LDPC lattices comparing to LDLCs, the complexity of our
schemes are significantly lower than the ones proposed for LDLCs. The
efficiency of the proposed schemes are presented using simulation results.
