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 nearcapacity performance in Gaussian TWRCs.