Compute-and-forward with relay selection: A cooperative game

Motivated by the cooperative game theory, we propose an efficient physical layer network coding technique for compute-and-forward (C&F) relaying systems, which jointly optimizes the sum and the minimum transmission rate, while minimizing the total transmitting power. Specifically, we show that relay selection in C&F networks leads to an increase of both rates. We also propose an algorithmic approach for the rates' further optimization and we illustrate that its implementation can offer the same or even greater gain than adding an extra relay. Furthermore, the tradeoff between the minimum and the sum rate is explained by utilizing the concept of Pareto frontier. Simulations and numerical results show that a combination of relay selection and the proposed algorithms offers a considerable increase in the sum rate for the same transmitting power, without reducing the system's Quality of Service.