Symmetric capacity of the Gaussian two-way relay channel to within 1/4e [nat]

The problem of reliable communication over the Gaussian two-way relay channel is considered and a new achievable rate region by combining structured lattice- and random Gaussian codes is presented. It is then demonstrated that the new bound can outperform previously known rate regions. In particular, having found the optimal time-sharing and power allocation policies, it is established that the proposed strategy achieves the symmetric capacity to within 1/4e ≈ 0.092 [nat] ≈ 0.133 [bit], which improves on earlier bounds.