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Block coding based on the discrete cosine transform (DCT) is very popular in image and video compression. Pre/post-filtering can be attached to a DCT-based block coding system to improve coding efficiency as well as to mitigate blocking artifacts. Previously designed pre/post-filters are optimized to maximize coding efficiency solely. For image and video communication over unreliable channels, those pre/post-filters are sensitive to transmission errors. This paper addresses the problem of designing pre/post-filters which are more error resilient. Reconstruction performance is measured by how low the average reconstruction error is, and how uniformly the reconstruction error is distributed. A family of pre/post-filters is designed to provide desired tradeoffs between coding efficiency and robustness to transmission errors. Experiments show that these filtering operators can achieve superior reconstruction performance without sacrificing much coding performance.