Recent advances in sparse graph codes have led to the proposal of fountain coding (FC). It becomes as an error correction coding scheme of choice for many multicasting and broadcasting systems. In this thesis, theoretical analysis, modeling and simulation of FC are presented for two different transmission schemes, namely, point-to-point and network coding (NC) transmission schemes. Network coding is used in order to gain throughput and some other advantages. Wireless networks with proposed combined FC and NC are modeled and simulated. The aim here is to use both coding techniques in such a way to improve the performance of the system. An intermediate node known as coding or relay node is used to perform the network coding within the whole network. The two transmission schemes are tested over different wireless channel models. These models represent different channel conditions and environments. The results of the tests have shown that combined FC & NC systems improves throughput over the original NC system without FC by more than (69%) without any loss in error performance at relatively low signal-to-noise power ratios (SNRs) and about 33% over the original FC system without NC at moderate and high SNRs. An optimum bit error rate performance (zero error) is achieved when applying FC to the original NC system without FC and throughput improvement is achieved when applying NC to the original FC system without NC, under different channel conditions.