Long Term Evolution-Advanced (LTE-A) and the evolved Multimedia Broadcast Multicast System (eMBMS) are the most promising technologies for the delivery of highly bandwidth demanding applications. In this paper we propose a green resource allocation strategy for the delivery of layered video streams to users with different propagation conditions. The goal of the proposed model is to minimize the user energy consumption. That goal is achieved by minimizing the time required by each user to receive the broadcast data via an efficient power transmission allocation model. A key point in our system model is that the reliability of layered video communications is ensured by means of the Random Linear Network Coding (RLNC) approach. Analytical results show that the proposed resource allocation model ensures the desired quality of service constraints, while the user energy footprint is significantly reduced.