  In the area of basic and network coded cooperative communication, 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 via time consuming Monte Carlo simulations, deriving
closed form expressions using approximations is crucial. In this work, the
ultimate goal is to derive an approximate average BER expression for a network
coded system. While reaching this goal, we firstly consider the cooperative
systems' instantaneous BER values that are commonly composed of Q-functions of
more than one variables. For these Q-functions, we investigate the convergence
characteristics of the sampling property and generalize this property to
arbitrary functions of multiple variables. Second, we adapt the equivalent
channel approach to the network coded scenario for the ease of analysis and
propose a network decoder with reduced complexity. Finally, by combining these
techniques, we show that the obtained closed form expressions well agree with
simulation results in a wide SNR range.
