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The underwater acoustic channel (UAC) is highly frequency selective; the degree of selectiveness depends on a detailed geometry of the channel. Further, the response changes over time as conditions affecting the response (such as water temperature, sea surface wind, salinity, etc.) are time-varying. A system design to deal with the frequency and time selective channel in UAC, therefore, becomes very challenging. We consider low density parity check (LDPC) coded orthogonal frequency division multiplexing (OFDM) system to deal with deep sub-band fading problems. In this paper, we aim to, first, provide a detailed realistic UAC model as we have noted that most LDPC coded OFDM systems have not been tested under realistic channels; second, to design a robust LDPC coded OFDM system; and third to test the proposed system under a variety of conditions using the channel model. We show robustness of the proposed system in simulation under a number of realistic channel conditions.