Analysis of the performance of network coding using the sampling property of Q-function

In the area of cooperative and network coded communication that naturally arises from cooperation, which become increasingly important in wireless communications, the expected end-to-end bit error rate (BER) values are frequently required to compare the proposed coding, relaying, and decoding techniques. Instead of obtaining these values through time consuming Monte Carlo simulations, deriving the closed form expressions via approximations is also crucial. In this work, we make use of the sampling property of the Q-function, which we commonly face while dealing with the related expectation integrals, in order to derive the end-to-end BER expressions for a network coded system. Furthermore, we show that the obtained expressions well agree with the simulation results.