One-level LDPC lattice codes for the relay channels

LDPC lattices were first family of lattices which have efficient decoding algorithm in high dimensions. An LDPC lattice can be constructed from Construction D´ and a number of nested LDPC codes. When we consider one code as underlying code of these lattices, one-level LDPC lattices will be obtained. In this paper we propose a new encoding and decoding method for one-level LDPC lattices. We also establish an efficient shaping method for these lattices based on hypercube shaping. Then, based on this encoding and decoding, we propose the implementation of block Markov encoding for one-way relay networks, using obtained one-level LDPC lattice codes. Our proposed decoding algorithm has lower complexity than those given for LDLC lattices.