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Lossless data compression systems are typically regarded as very brittle to transmission errors. This limits their applicability to domains like noisy tetherless channels or file systems that can possibly get corrupted. Here we show how a popular lossless data compression scheme used in file formats GIF, PDF, and TIFF, among others, can be made error-resilient in such a way that the compression performance is minimally affected. The new scheme is designed to be backward-compatible, that is, a file compressed with our error-resilient algorithm can be still decompressed by the original decoder. In this preliminary report, we present our scheme, collect some experimental data supporting our claims, and provide some theoretical justifications.