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This paper presents an improved technique for estimating the end-to-end distortion, which includes both a quantization error after encoding and a random transmission error, after transmission in video communication systems. The proposed technique mainly differs from most existing techniques in that it takes into account filtering operations, e.g., interpolation in subpixel motion compensation, as introduced in advanced video codecs. The distortion estimation for pixels or subpixels under filtering operations requires the computation of the second moment of a weighted sum of random variables. In this paper, we prove a proposition for calculating the second moment of a weighted sum of correlated random variables without requiring knowledge of their probability distribution. Then, we apply the proposition to extend our previous error-resilient algorithm for prediction mode decision without significantly increasing complexity. Experimental results using an H.264/AVC codec show that our new algorithm provides an improvement in both rate-distortion performance and subjective quality over existing algorithms. Our algorithm can also be applied in the upcoming high-efficiency video coding standard, where additional filtering techniques are under consideration.