Energy efficient and low complex wireless communication

Network coding designs over GF(q) spans an extensive range of research directions covering a wide range of applications. Galois field used for network coding should be a function of the total number of nodes in the networks. Thus, the larger the number of sources and relays the larger the Galois field, while keeping the same diversity order in relay-aided transmission. Furthermore, the modulation order and the Galois field are the same and this solution introduces a constraint on achievable rate and decoding complexity as network code and modulation cannot be chosen independently. In order to overcome this important limitation, in this paper we propose a splitting based approach where network coding and modulation are not necessarily the same. Our results show that if the modulation order is smaller than the Galois field; we are still able to achieve the same diversity order with lower decoding complexity.