Belief propagation is a popular global optimization technique for many computer vision problems. However, it requires extensive computation due to the iterative message passing operations. In this paper, we present a new process element (PE) for efficient message construction. The efficiency is gained by exploiting the unique characteristics of the generalized Potts model (truncated linear mode) of the smoothness term in the Markov random field. For stereo estimation with L disparity values, the algorithm successfully reduces the computation from O(L2 ) to O(L) and retains the high throughput and low latency. Compared with the direct message construction PE, our method achieves 87.14% computation saving and a 94.38% PE area reduction.