LDPC Lattice Codes for Full-Duplex Relay Channels
  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. 
Hassan Khodaiemehr and Dariush Kiani and Mohammad-Reza Sadeghi
cs.IT math.IT