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We investigate performance limits of a coded asymmetric OFDM (A-OFDM) system in multipath fading channels when maximum-likelihood (ML) detection is deployed. Our A-OFDM formulation is general and the analysis extends to coded OFDM (COFDM), precoded COFDM and single carrier systems. At first, an exact pairwise error probability is evaluated based on Craig's alternative form of the Q-function. Then we derive a tight union bound of bit error probability based on a code transfer function. The analysis shows that the coded A-OFDM system has improved diversity, whose order equals to the channel code's Hamming distance times the fast Fourier transform (FFT) or inverse FFT (IFFT) size of the A-OFDM system. The simulation results support the analysis and demonstrate superior performance of the coded A-OFDM system with the high signal to noise ratio (SNR).