Coding for Parallel Gaussian Bidirectional Relay Channels: A Deterministic Approach

We study the capacity region of the parallel Gaussian bidirectional relay channel with L independent subchannels and propose efficient coding schemes for approaching the capacity limit within a constant gap. A two-step approach is considered. First, the corresponding finite field linear deterministic model is studied, for which linear network coding across sub-channels is shown to achieve the capacity region of the channel. Next, based on the insight obtained, a lattice-based compute-and-forward scheme together with simple linear network coding across sub-channels is proposed and is shown to achieve the capacity region of the Gaussian model to within L bits per user regardless of the channel parameters. Even though coding across different sub-channels is necessary for approaching the capacity region, it is shown that this can be realized through a simple linear network coding scheme ( across different sub-channels) at the relay.