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This paper deals with the sub-carrier and bit allocations for multi-user orthogonal frequency division multiplexing (OFDM) systems by a modified particle swarm optimization (MPSO) method for a specific bit error rate (BER). The resources (subcarriers and the number of bits per symbol per subcarrier) are allocated according to the instantaneous channel state information (CSI) which is assumed to be perfect and available with no latency and at no cost. To allocate the resources, we optimize total transmit power and throughput simultaneously with MPSO for a multi-user OFDM system. Simulation results show that for a large number of users, the MPSO performs better than existing algorithms, and that joint optimization (margin adaptive and rate adaptive) converges quickly.