This paper presents a novel and fast approach for ground plane segmentation in a LiDAR point cloud, specifically optimized for processing speed and hardware efficiency on FPGA hardware platforms. Our approach leverages a channel-based segmentation method with an advanced angular data repair technique and a cross-eight-way flood-fill algorithm. This innovative approach significantly reduces the number of iterations while ensuring the high accuracy of the segmented ground plane, which makes the stream-based hardware implementation possible. To validate the proposed approach, we conducted extensive experiments on the SemanticKITTI dataset. We introduced a bird's-eye view (BEV) evaluation metric tailored for the area representation of LiDAR segmentation tasks. Our method demonstrated superior performance in terms of BEV areas when compared to the existing approaches. Moreover, we presented an optimized hardware architecture targeted on a Zynq-7000 FPGA, compatible with LiDARs of various channel densities, i.e., 32, 64, and 128 channels. Our FPGA implementation operating at 160 MHz significantly outperforms the traditional computing platforms, which is 12 to 25 times faster than the CPU-based solutions and up to 6 times faster than the GPU-based solution, in addition to the benefit of low power consumption.