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Given the critical role of motion estimation (ME) in a video coder, testing such a module is of priority concern. While focusing on the testing of ME in a video coding system, this work presents an error detection and data recovery (EDDR) design, based on the residue-and-quotient (RQ) code, to embed into ME for video coding testing applications. An error in processing elements (PEs), i.e. key components of a ME, can be detected and recovered effectively by using the proposed EDDR design. Experimental results indicate that the proposed EDDR design for ME testing can detect errors and recover data with an acceptable area overhead and timing penalty. Importantly, the proposed EDDR design performs satisfactorily in terms of throughput and reliability for ME testing applications.