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The paper studies the problem of finding an optimal subcarrier and power allocation strategy for downlink communication to multiple users in an orthogonal-frequency-division multiplexing-based wireless system. The problem of minimizing total power consumption with constraints on bit-error rate and transmission rate for users requiring different classes of service is formulated and simple algorithms with good performance are derived. The problem of joint allocation is divided into two steps. In the first step, the number of subcarriers that each user gets is determined based on the users' average signal-to-noise ratio. The algorithm is shown to find the distribution of subcarriers that minimizes the total power required when every user experiences a flat-fading channel. In the second stage of the algorithm, it finds the best assignment of subcarriers to users. Two different approaches are presented, the rate-craving greedy algorithm and the amplitude-craving greedy algorithm. A single cell with one base station and many mobile stations is considered. Numerical results demonstrate that the proposed low complexity algorithms offer comparable performance with an existing iterative algorithm.