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In this letter, resource allocation in a downlink orthogonal frequency division multiplexing (OFDM)-based non-orthogonal multiple access (NOMA) system is studied. We investigate an optimization problem of minimizing the total transmit power under quality of service requirements, by jointly searching for optimal subcarrier assignments of each user and power allocations over subcarriers. We first present an optimal solution of power allocation with fixed subcarrier assignments, based on which we next propose a low-complexity algorithm of jointly optimizing the subcarrier assignments and power allocations. Numerical results show that the performance of the proposed algorithm is near-optimal and the power consumption is significantly reduced compared with both the conventional OFDM-based frequency division multiple access and the static NOMA resource allocation schemes.