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In this paper, we present a power assignment mechanism which is suitable for orthogonal frequency division multiplexing (OFDM)-based underwater acoustic communication system. An essential feature of this scheme is that higher power is allocated to the information that requires higher quality of service. To achieve the purpose of maximum resource utilization, or minimum total transmission power, we also incorporate unequal error protection and adaptive modulation techniques into the proposed power assignment scheme. Specifically, we employ high power, low level modulation, and high level error protection scheme for messages that dictate stringent bit error rate (BER). For a practical underwater acoustic communication scenario, a simulation has been carried out to verify proper functioning of the proposed scheme.