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This work introduces a rate allocation method for the transmission of pre-encoded JPEG2000 video over time-varying channels, which vary their capacity during video transmission due to network congestion, hardware failures, or router saturation. Such variations occur often in networks and are commonly unpredictable in practice. The optimization problem is posed for such networks and a rate allocation method is formulated to handle such variations. The main insight of the proposed method is to extend the complexity scalability features of the FAst rate allocation through STeepest descent (FAST) algorithm. Extensive experimental results suggest that the proposed transmission scheme achieves near-optimal performance while expending few computational resources.