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Average profile of the Lempel-Ziv scheme for a Markovian source

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2 Author(s)
Jing Tang ; Appl. Microsyst. Corp., Redmond, WA, USA ; Szpanskowski, W.

We consider the Lempel-Ziv (1978) parsing scheme (LZ'78) which parses a sequence into phrases such that the next phrase is the shortest phrase not seen in the past. Two models called further digital tree model and Lempel-Ziv model are of interest. The former asks for the length of the Lempel-Ziv string composed of m phrases. The latter assumes that the string is of fixed length, say n, and investigates the number of phrases generated by the scheme. We are interested in the average profile which is defined as the average number of phrases of a given size. The average profile is related to the length of a randomly selected phrase which we denote either as Dm, for the digital tree model or as DnLZ for the Lempel-Ziv model. Thus, we concentrate on studying Dm, and DnLZ . More precisely, we investigate the fine structure (i.e., second-order properties) of these parameters for a Markovian source over a finite alphabet Σ of size V

Published in:

Information Theory. 1997. Proceedings., 1997 IEEE International Symposium on

Date of Conference:

29 Jun-4 Jul 1997