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We propose a novel video codec that can distribute computational complexity between the encoder and the decoder in a flexible manner. Since motion estimation is the most computationally intensive part in video coding, it is important to share the motion estimation task. In the proposed algorithm, the decoder estimates motion vectors by performing a partial three step search. The estimated motion vectors are sent back to the encoder via a feedback channel. The encoder then refines the received motion vectors. In this work, four operation modes corresponding to the encoder to decoder complexity ratios are presented. Experimental results demonstrate that the proposed algorithm allocates the complexity between the encoder and the decoder effectively, while providing promising compression performance.