3GPP's Long Term Evolution (LTE) represents the one of the most valuable alternatives to offer a wireless broadband access in fully mobile network context. In particular LTE is able to manage several communication flows characterized by different QoS constrains. This paper deals with a network topology where the mobile users are clustered in Multicast Groups and the base station broadcasts a different traffic flow to each cluster. In order to improve the network throughput on a per-user basis, all communications rely on a Random Linear Network Coding (RLNC) scheme. A key aspect in the QoS management is represented by the power adaptation strategy in use. This paper proposes a novel convex formulation to the power adaptation problem for the downlink phase taking into account the specific RLNC scheme adopted by each communication flow. By the proposed convex formalization, an optimal solution of the problem can be early found in real time. Moreover, the proposed power adaptation strategy shows good performance for what concern throughput and fairness among the users when compared with other alternatives.