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Because of its promising scalability potential and support of multilevel per cell storage, phase-change memory has become a topic of great current interest. However, recent studies show that structural relaxation effect makes the resistance of phase-change material drift over the time, which can severely degrade multilevel per cell phase-change memory storage reliability. This makes powerful memory fault tolerance solutions indispensable, where error correction code (ECC) will play an essential role. This work aims to develop fault tolerance solutions that can effectively compensate memory cell resistance drift. First, based upon information-theoretical study, we show that conventional use of ECC, which is unaware of memory content lifetime, can only achieve the performance with a big gap from the information-theoretical bounds. This motivates us to study the potential of time-aware memory fault tolerance, where the basic idea is to keep track the memory content lifetime and use this lifetime information to accordingly adjust how memory cell resistance is quantized and interpreted for ECC decoding. Under this time-aware fault tolerance framework, we study the use of two types of ECCs, including classical codes such as BCH that only demand hard-decision input and advanced codes such as low-density parity-check (LDPC) codes that demand soft-decision probability input. Using hypothetical four-level per cell and eight-level per cell phase-change memory with BCH and LDPC codes as test vehicles, we carry out extensive analysis and simulations, which demonstrate very significant performance advantages of such time-aware memory fault tolerance strategy in the presence of significant memory cell resistance drift.