In this paper, we study multicasting multiple description traffic to a group of mobile stations (MSs). The traffic is pre‐cached at a number of access points (APs), and the MSs have different quality requirements in terms of number of required descriptions. Each AP transmits one description and forms a single‐hop multicast group to reach a certain number of MSs. Different APs can transmit the same or different descriptions. MSs requiring multiple descriptions should be covered by at least the same number of the APs that transmit different descriptions. We study two problems, description assignments, and power allocations. The former is to assign a description for each AP, and the latter is to allocate the transmission power for each AP. Two objectives are considered subject to satisfying the requirements of the MSs, one is to minimize the total transmission power of all the APs, and another is to minimize the maximum transmission power of the APs. For each objective, a centralized and a distributed scheme are proposed, and their performance is compared with the optimum. Numerical results show very good performance of the heuristic schemes. Copyright © 2016 John Wiley & Sons, Ltd.