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Hardware implementation of data compression algorithms is receiving increasing attention due to exponentially expanding network traffic and digital data storage usage. In this paper, we propose several serial one-dimensional and parallel two-dimensional systolic-arrays for Lempel-Ziv data compression. A VLSI chip implementing our optimal linear array is fabricated and tested. The proposed array architecture is scalable. Also, multiple chips (linear arrays) can be connected in parallel to implement the parallel array structure and provide a proportional speedup.