Irregular repeat-accumulate coded physical-layer network coding design for two-way relay channels

We propose a new irregular repeat-accumulate (IRA) coded physical-layer network coding (PNC) scheme for Gaussian two-way relay channels (TWRCs). In the scheme, a same random-coset IRA code over GF(q) is employed at the two users, which directly maps the q-ary message sequences into coded q-PAM symbol sequences. The relay computes the network coded message sequence directly from the superimposed signal using an iterative belief propagation algorithm. By exploring the symmetry and permutation-invariance properties of the decoder's soft information distribution, a two-dimension extrinsic information transfer (EXIT) chart is developed to analyze and optimize the nonbinary IRA coded PNC scheme. Numerical results demonstrate that our developed scheme achieves near-capacity performance in Gaussian TWRCs.