LDPC Lattice Codes for Full-Duplex Relay Channels

Low-density parity-check (LDPC) lattices were the first family of lattices to show efficient decoding in high dimensions. We consider a case of these lattices with one binary LDPC code as an underlying code. We employ encoding and decoding of the LDPC lattices in a cooperative transmission framework. We establish two efficient shaping based on hypercube 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. An efficient method is also required 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 code (LDLC) lattices. Due to the lower complexity of the decoding for LDPC lattices comparing with LDLCs, the complexity of our schemes is significantly lower than the ones proposed for LDLCs. The efficiency of the proposed schemes is presented using simulation results that indicate the outperforming behavior of LDLCs over LDPC lattice codes in the same dimensions. However, having lower decoding complexity enables us to increase the dimension of the lattice to compensate the existing gap between the performance of the LDPC lattice codes and the LDLCs.

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