In wireless sensor networks, network lifetime is among the most important criteria. Network lifetime mainly depends on the link scheduling established at the Medium Access Control layer. Indeed, the avoidance of transmission conflicts enables energy savings since there are no message retransmissions. We are interested in deterministic allocation of the wireless medium for data collection in tree based sensor networks. In this paper, we consider a generalization of the distance 2-edge coloring problem, in which transmission and interference edges are taken into account. We propose a distributed algorithm for this problem, called D2EC, which ensures that conflicts are avoided. We also carry out simulations to compare D2EC with a random allocation strategy of the wireless medium. The simulation results show that there is a significant reduction on packet loss by using D2EC. Moreover, D2EC extends the lifetime of 250% in the best case regarding the random allocation of the wireless medium.