Network Coding was introduced to the communication world in 2000. In contrast with the routing, in which the nodes just put the packets on thecorrect links, this theory allows the nodes to do some operations on the packets that result in increasingthroughput, decreasing the error and improving the performance of the network. In this thesis, aspecial justify; MARGIN: 0cm 0cm 8pt" In this regard, in this thesis, after reviewing the network coding concepts,non-block based network codes are introduced and a special model of them, which is used in broadcast channels is explained. Then, we extend this model to the relay network and calculate the delivery rateanalytically and compare it with the simulation results.Despite using simplifying approximations in the system analysis, the results of the calculation match the simulation. Spec ially the results are more accurate for modest number of the receivers.It is worth mentioning that this coding method is capable of reaching multi-rate packet delivery.In the other words, it can deliver packets to each receiver based on its channel quality.Whereas, the common and popular Random linear codes do not have this feature and we show it by simulation. Key words: Network coding, Deterministic non-block based network coding, Broadcast network, Relay network,Delivery rate, Multi-rate packet delivery
