#### Performance Analysis of Network Coded Systems Under Quasi-static Rayleigh Fading Channels

##### Tugcan Aktas, A. Ozgur Yilmaz, Emre Aktas

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.

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