Physical network coding for TWR channel: Capacity region and error exponents

Two way relay channel (TWRC) is being proposed as a competitive strategy for data transmission in cooperative networks. The capacity region of this model has been recently extensively investigated and achievable bounds are derived based on the cut-set theorem and decode and forward relaying strategy. However, capacity limits that have been derived assume infinite block length which is impractical for real approaches. We present in this contribution a new information-theoretic framework to reconstruct the maximum achievable rate region in the TWRC by taking into account fixed block length and physical network coding. In particular, individual error probabilities are treated using random error exponents. We characterize the rate region for discrete memoryless channel by using optimal time division between links and constrained error probabilities. We evaluate the system performance for different SNR regimes with/without power control. All results are generalized to additive white Gaussian network with power constraints.