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In this paper, computation reduction algorithms of motion estimation are developed for low rate video coders. By jointly considering motion estimation, discrete cosine transform, and quantization, the all-zero and zero-motion detection algorithms are suggested to reduce the computation of motion estimation. Simulation results show that many unnecessary computations in motion estimation are greatly reduced. For the Akiyo sequence, the proposed algorithms reduce the average numbers of search points from 28.90 and 4.99 to 2.89 and 1.40 for three-step search and diamond-search algorithms, respectively.