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We present a cross-layer resource-allocation (RA) scheme for the downlink in orthogonal frequency-division multiple-access (OFDMA) systems with fairness control among the users, where the resources to be allocated are power, bits per symbol, and subchannels. The use of subchannels, which are defined as group of subcarriers, leads to reducing the complexity of the bandwidth allocation compared with the commonly adopted subcarrier allocation. A goodput-based optimization function, which is derived by combining automatic repeat request (ARQ) and physical (PHY)-layer parameters, is used to perform RA for applications that demand error-free transmissions. Two transmission strategies are considered, with and without concatenation of subchannels, for which two different RA methods are developed, respectively. We also propose an algorithm that improves the complexity associated to both concatenation and nonconcatenation schemes, without appreciable performance loss.