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Compressed memory system is a high performance memory system that is capable to reduce memory size and improve memory performance. This project focuses on the memory management of compressed memory and a secondlevel memory and compares different compress memory allocation algorithms. Two dynamic memory allocation algorithms, which are lazy-fit and link-fit algorithms are analyzed to determine their impacts on memory compression and memory access time. In this work, systemC design approach is used to design the compressed memory system. The compressed memory system is designed from C modeling and refined to systemC register-transfer level abstraction. The simulation results show the lazy-fit system has better allocation speed compared to the one based on link-fit algorithm.