Capacity Bounds for Two-Way Relay Channels

We provide achievable rate regions for two-way relay channels (TRC). At first, for a binary TRC, we show that the subspace-sharing of linear codes can achieve the capacity region. And, for a Gaussian TRC, we propose the subset-sharing of lattice codes. In some cases, the proposed lattice coding scheme can achieve within 1/2-bit the capacity and is asymptotically optimal at high signal-to-noise ratio (SNR) regimes.