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In this paper, we present a general 2-D multiple-access scheme, namely, code time division multiple access (CTDMA), on the downlink of multicarrier communication systems. CTDMA combines the idea of CDMA in the code domain and TDMA in the time domain. We consider suitable resource allocation strategies with our CTDMA scheme in the code domain and the time domain jointly. Under the total transmission-power minimization criterion, we propose a near optimal approach to allocate codes and transmission time to users appropriately, while the data rate of each user is guaranteed. To reduce the computational complexity, we also give some simplified suboptimal approaches for certain types of systems, namely, the one-to-one approach for the fully loaded system and the multiple-to-one approach for the nonfully loaded systems. To check the differences between our approaches and the optimal allocation strategy, we derive a pair of lower and upper bounds on the optimal resource allocation solution. Simulation results show that major improvement can be obtained by the near optimal approach, while the suboptimal approaches only cause minor performance degradation. We also show that our approaches will all converge to the lower bound as well as the optimal allocation solution, when the system size increases.