Improved GA solution on LNC coefficient matrix for multi-user cooperative communication

Cooperative communication with network coding can yield higher system diversity gain and improve the efficiency of cooperation, for which designing the proper and efficient coding coefficients is one key technique for implementation. The important contributions of our work reveal the existence of coding coefficient matrix of order M constructed in GF(M = 2ⁿ) and propose practical and effective method to search such matrix. An improved genetic algorithm solution is proposed by introducing the local gradient search mechanism for large searching space and the search results show that the proposed method can obtain satisfying solutions and better computing performance for M = 8 in GF(8). The discussion on improved local gradient search mechanism illustrates its underlying potentials in global search framework. This work gains an insight into the coefficient matrix construction for cooperative communication with network coding in GF(2ⁿ).