Using a multiple-relay cooperative communication network is one of the most effective methods for reducing the impact of fading on wireless channels. In such a network, a source sends information to a destination via several nearby nodes, which form virtual antennas regardless of the size and cost of the mobile equipment. The network is also required to transmit multimedia and allow access to high-speed data, thus requiring significant energy consumption. Until now, mobile devices have only been able to store a limited amount of energy, leading to rapid battery depletion in relay and mobile user devices. Moreover, the Base Station (BS) itself consumes considerable energy and the number of BSs continues to grow. Therefore, the development of an energy-efficient cooperative communication network that reduces energy consumption while maintaining the highest possible level of performance is urgently required. To this end, this paper proposes the application of Hamming coding to a multiple-relay cooperative communication network for Energy Efficiency (EE) analysis. Then, the relay protocol aspect is also determined to increase the level of EE. This study considers two practical protocol relays, Amplify-and-Forward (AF) and Quantize-and-Forward (QF), for a more in-depth analysis of EE. The results show that the multiple-relay QF network demonstrates EE when compared to a multiple-relay AF network.