Noisy analog network coding for the two-way relay channel

An achievable rate region based on Shannon´s inner bound is given for the two-way relay channel. The relaying scheme operates on noisy received signals and generates new analog values to be transmitted to a destination. The scheme is therefore referred to as noisy analog network coding. The achievable rates are then optimized for a Gaussian two-way relay channel, when the relay is memoryless (this type of relaying is also known as instantaneous relaying). For one particular instance of the channel when the received signal at the relay is noiseless, it is shown that instantaneous noisy analog network coding can be optimal. For the noisy case, a numerical optimization algorithm is presented in order to optimize the instantaneous coding strategy. The optimized analog mapping turns out to be nonlinear and periodic. Finally, it is demonstrated that the achievable rates associated with optimized mappings can outperform those achieved by linear relaying, compress-and-forward, and can operate close to the recently proposed noisy network coding scheme.