Lattice-based Wyner-Ziv coding for parallel Gaussian two-way relay channels

Parallel two-way relay channel models a cooperative communication scenario where a relay helps two terminals to exchange their messages over independent Gaussian channels. For the single channel case, we have shown previously that lattice-based physical layer network coding achieves the same rate as compress-and-forward scheme with a random coding strategy. A direct extension of this lattice-based scheme to parallel Gaussian channel is to repeat the same strategy for each subchannel. However this approach is not scalable with the number of sub-channels since the complexity of the scheme becomes prohibitive when a large number of sub-channels is employed. In this contribution, we investigate a lattice-based physical layer network coding scheme where the relay jointly processes all the sub-channels together. We characterize the rate region allowed by our coding scheme and assess the performance penalty compared to the separate channel processing approach.