Automatic modulation classification (AMC) techniques enable the estimation of the bit allocation table in adaptive orthogonal frequency division multiplexing (OFDM) systems. In this study, the authors investigate the classification performance of a low‐complexity maximum‐a‐posteriori (MAP) algorithm for AMC. Also, they derive an approximation of the probability of classification error in a subcarrier for this classifier. Furthermore, based on these theoretical derivations, a novel modified rate adaptive (RA) bit loading algorithm with additional classification error constraint is proposed. Numerical results show that the authors’ proposed method outperforms the RA algorithm significantly in terms of classification performance, while providing reasonable data throughput specifically at higher signal‐to‐noise ratios.