The underwater channel is known to offer poor communications channel. The channel medium is highly absorptive and the transmission bandwidth is limited. In addition, the channel is highly frequency selective; the degree of selectiveness depends on a detailed geometry of the channel. Furthermore, the response changes over time as the channel conditions affecting the response such as water temperature, sea surface wind and salinity are time-varying. The transceiver design to deal with the frequency and time selective channel, therefore, becomes very challenging. It has been known that deep fading at certain specific sub-carriers are detrimental to OFDM systems. To mitigate this negative effect, the proposed coded OFDM system employs an LDPC code based modulation. In this paper, we aim 1) to provide a detailed underwater channel model; 2) to design a robust LDPC coded OFDM system; 3) to test the proposed system under a variety of channel conditions enabled by the channel model.