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We propose an adaptive hybrid automatic repeat request--forward error correction (ARQ--FEC) erasure-correcting scheme for quality of service (QoS)-driven mobile multicast services over wireless networks. The main features of our proposed scheme include (i) the low complexity achieved by the graph code; (ii) dynamic adaptation to the variations of packet-loss level and QoS requirements. To increase error-control efficiency and support diverse QoS requirements, we develop a two-dimensional (2-D) adaptive error-control scheme that dynamically adjusts not only the error-control redundancy, but also the code mapping structures. By deriving and identifying the closed-form nonlinear analytical expression between the optimal check-node degree and the packet-loss level, we propose the nonuniformed adaptive coding structures to achieve high error-control efficiency. Applying the Markov chain model, we obtain closed-form expressions that derive the error-control redundancy as a function of packet-loss level and the optimal check-node degree in each adaptation step. The convergency of error-control redundancy adaptation is dynamically controlled by different QoS requirements such that a high error-control efficiency can be achieved. Using the proposed 2-D adaptive error control, we design an efficient hybrid ARQ--FEC protocol for mobile multicast services with diverse reliability QoS requirements. The proposed scheme keeps the feedback overhead low by consolidating only the numbers rather than the sequence numbers of the lost packets, which are fed back by multicast receivers. Also conducted is a set of numerical and simulation evaluations that analyze and compare our proposed adaptive scheme with those using nonadaptive graph codes, Reed--Solomon erasure codes (RSE), and the pure ARQ-based approach. The simulation results show that our proposed scheme can efficiently support QoS-driven mobile multicast services and achieve high error-control efficiency while imposing low error-control complexity and overhead for mobile multicast networks. Index Terms--Adaptive hybrid automatic repeat request-forward error correction (ARQ--FEC), error control, graph codes, low-complexity erasure codes, mobile multicast, quality of service (QoS), wireless networks.