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Ever since the wireless relay network (RN) was introduced, it has led to the discovery of several new protocols, which have been consistently improved by researchers to overcome many constraints such as throughput, capacity bound, symbol error rate, outage probability, and power allocations. Meanwhile, network coding (NC) was invented as an efficient technique to address these problems. To the best of our knowledge, there has been no comprehensive discussion about wireless-RN modes in the literature. We therefore provide a tutorial concerning the basic concepts of NC, dealing with the classification of particular relay modes, and presenting new wireless-RN protocols with/without NC in this paper. Under appropriate categories (i.e., fixed and dynamic), much attention has been given to various proposed wireless-RN protocols because they may differ individually depending on their processing at relay …