Irregular Repeat-Accumulate Lattice Network Codes for Two-Way Relay Channels

We propose and design a lattice coded physical- layer network coding (PNC) over a finite complex number field Z[ω]ξZ[ω] in a two-way relay channel (TWRC). In our design, we construct the lattice codes from an irregular repeat- accumulate (IRA) code over GF(q). A randomly generated coset is employed to our scheme to ensure that the codes exhibit permutation invariance and symmetric properties. In a TWRC, two users employ the same lattice codebook and use the same transmit power. The relay attempts to decode the lattice coded network codes of the two users' messages by using an iterative belief propagation decoder and then broadcasts the lattice network coded messages back to both users. We use extrinsic information transfer (EXIT) charts to analyse the convergence behaviour and optimise the decoding threshold. Our results show that the optimised IRA lattice network codes can provide significant coding gain over the previous designed lattice coded PNC scheme over one dimensional Z lattice.