# The Sliding-Window Lempel-Ziv Algorithm is Asymptotically Optimal

• A. D. Wyner
• J. Ziv
Part of the The Springer International Series in Engineering and Computer Science book series (SECS, volume 276)

## Abstract

The sliding-window version of the Lempel-Ziv data-compression algorithm (sometimes called LZ ‘77) has been thrust into prominence recently. This is the algorithm used in the highly successful “Stacker” program for personal computers. It is also incorporated into Microsoft’s new MS-DOS-6. Although other versions of the Lempel-Ziv algorithm are known to be optimal in the sense that they compress a data-source to its entropy, optimality in this sense has never been demonstrated for this version.

In this paper, we will describe the algorithm, and show that as the “window-size”, a quantity which is related to the memory and complexity of the procedure, goes to infinity, the compression rate approaches the source entropy. The proof is surprisingly general, applying to all finite alphabet stationary ergodic sources.

Entropy Prefix

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### Referecnes

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