Point-wise analysis of redundancy in SWLZ algorithm for φ-mixing sources

Author

Jain, Ayush ; Bansal, Rakesh K.

Author_Institution

Indian Inst. of Technol. Kanpur, Kanpur, India

fYear

2015

fDate

April 26 2015-May 1 2015

Firstpage

1

Lastpage

5

Abstract

In this paper, we bound the number of phrases of the sliding window Lempel-Ziv (SWLZ) algorithm using an upper bound on the expected number of phrases in the fixed database Lempel-Ziv (FDLZ) algorithm for a class of φ-mixing sources which includes Markov sources, unifilar sources and finite state sources as special cases, as developed by Yang and Kieffer [1]. We use this bound to obtain a point-wise upper bound on the redundancy rate of SWLZ algorithm to be 2H(log₂log₂n_w/log₂n_w) + O(log₂log₂log₂n_w/log₂n_w). Here H is the entropy rate of the source and n_w is the window size.

Keywords

Markov processes; entropy; φ-mixing sources; 2H(log₂log₂n_w/log₂n_w); FDLZ algorithm; Markov sources; O(log₂log₂log₂n_w/log₂n_w); SWLZ algorithm; entropy rate; finite state source; fixed database Lempel-Ziv algorithm; point-wise analysis; point-wise upper bound; redundancy rate; sliding window Lempel-Ziv algorithm; unifilar source; window size; Algorithm design and analysis; Databases; Electronic mail; Markov processes; Mathematical model; Redundancy; Upper bound; φ-mixing processes; LZ77; Markov processes; almost sure convergence; fixed database Lempel-Ziv (FDLZ); point-wise redundancy rate; sliding window Lempel-Ziv (SWLZ);

fLanguage

English

Publisher

ieee

Conference_Titel

Information Theory Workshop (ITW), 2015 IEEE

Conference_Location

Jerusalem

Print_ISBN

978-1-4799-5524-4

Type

conf

DOI

10.1109/ITW.2015.7133103

Filename

7133103