The sliding-window Lempel-Ziv algorithm is asymptotically optimal

The sliding-window version of the Lempel-Ziv data-compression algorithm (sometimes called LZ '77) has been thrust into prominence recently. A version of this algorithm is used in the highly successful "Stacker" program for personal computers. If is also incorporated into Microsoft...

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Vydáno v:Proceedings of the IEEE Ročník 82; číslo 6; s. 872 - 877
Hlavní autoři: Wyner, A.D., Ziv, J.
Médium: Journal Article
Jazyk:angličtina
Vydáno: IEEE 01.06.1994
Témata:
Artificial intelligence
Data compression
Encoding
Entropy
H infinity control
Jacobian matrices
Microcomputers
Modems
Random sequences
Statistics
ISSN:0018-9219
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Shrnutí:The sliding-window version of the Lempel-Ziv data-compression algorithm (sometimes called LZ '77) has been thrust into prominence recently. A version of this algorithm is used in the highly successful "Stacker" program for personal computers. If is also incorporated into Microsoft's new MS-DOS-6. Although other versions of the Lempel-Ziv algorithm are known to he 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 self-contained 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.< >
ISSN:0018-9219
DOI:10.1109/5.286191