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Many papers have shown that low density parity-check (LDPC) codes exhibit excellent performance in the additive white noise (AWGN) channel and flat fading channels, but their performance on frequency-selective fading channels slightly degrades. In this paper, we present the construction of a new algebraic geometric LDPC code and its decoding algorithm, evaluate the performance of AG density parity-check codes in frequency-selective fading channels based on the Overlapped code division multiple access (OVCDMA) system. Simulation results show that AG-LDPC codes outperform turbo codes at high signal-to-noise ratio (SNR) over a wild range of mobile speeds. Furthermore we simply analyze the reasons on their differences on performance, indicating that the distance spectrum plays a very important role to the performance of codes.