Recently, a higher dimensional Eisenstein-Jacobi networks, has been proposed in [22], which is shown that they have better average distance with more number of nodes than a single dimensional EJ networks. Some communication algorithms such as one-to-all and all-to-all communications are well known and used in interconnection networks. In one-to-all communication, a source node sends a message to every other node in the network. Whereas, in all-to-all communication, every node is considered as a source node and sends its message to every other node in the network. In this paper, an improved one-to-all communication algorithm in higher dimensional EJ networks is presented. The paper shows that the proposed algorithm achieves a lower average number of steps to receiving the broadcasted message. In addition, since the links are assumed to be half-duplex, the all-to-all broadcasting algorithm is divided into three phases. The simulation results are discussed and showed that the improved one-to-all algorithm achieves better traffic performance than the well-known one-to-all algorithm and has 2.7% less total number of senders