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This paper advocates a time-aware design methodology for using multilevel per cell (MLC) phase-change memory (PCM) in data storage systems such as solid-state disk and disk cache. It is well known that phase-change material resistance drift gradually reduces memory device noise margin and degrades the raw storage reliability. Intuitively, due to the time-dependent nature of resistance drift, if we can dynamically adjust storage system operations adaptive to the time and, hence, memory cell resistance drift, we may improve various PCM-based data storage system performance metrics. Under such an intuitive time-aware system design concept, we propose three specific design techniques, including time-aware variable-strength error correction code (ECC) decoding, time-aware partial rewrite, and time-aware read-&-refresh. Since PCM-based data storage systems have to use powerful ECC whose decoding can be energy-hungry, the first technique aims to minimize the ECC decoding energy consumption. The second technique improves the data retention limit when using partial rewrite in MLC PCM, and the third technique can further improve the efficiency of time-aware variable-strength ECC decoding. Using hypothetical 2-bit/cell PCM with device parameters from recent device research as a test vehicle, we carry out mathematical analysis and trace-based simulations, which show that these techniques can improve the data retention limit by few orders of magnitude, and enable up to 97 and 79 percent energy savings for PCM-based solid-state disk and PCM-based disk cache.