This paper presents segment-parallel prediction for high-throughput compression and decompression of floating-point data streams on an FPGA-based LBM accelerator. In order to enhance the actual memory I/O bandwidth of the accelerator, we focus on the prediction-based compression of floating-point data streams. Although hardware implementation is essential to high-throughput compression, the feedback loop in the decompressor is a bottleneck due to sequential predictions necessary for bit reconstruction. We introduce a segment-parallel approach to the 1D polynomial predictor to achieve the required throughput for decompression. We evaluate the compression ratio of the segment-parallel cubic prediction with various encoders of prediction difference.