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Error-bounded lossy compression is becoming more and more important to today's extreme-scale HPC applications because of the ever-increasing volume of data generated because it has been widely used in in-situ visualization, data stream intensity reduction, storage reduction, I/O performance improvement, checkpoint/restart acceleration, memory footprint reduction, etc. Although many works have optimized ratio, quality, and performance for different error-bounded lossy compressors, there is none of the existing works attempting to systematically understand the impact of lossy compression errors on HPC application due to error propagation. In this paper, we propose and develop a lossy compression fault injection tool, called LCFI. To the best of our knowledge, this is the first fault injection tool that helps both lossy compressor developers and users to systematically and comprehensively understand the impact of lossy compression errors on HPC programs. The contributions of this work are threefold: (1) We propose an efficient approach to inject lossy compression errors according to a statistical analysis of compression errors for different state-of-the-art compressors. (2) We build a fault injector which is highly applicable, customizable, easy-to-use in generating top-down comprehensive results, and demonstrate the use of LCFI. (3) We evaluate LCFI on four representative HPC benchmarks with different abstracted fault models and make several observations about error propagation and their impacts on program outputs.