Efficient universal lossless data compression algorithms based on a greedy sequential grammar transform .2. With context models

For pt. I see ibid., vol.46, p.755-88 (2000). The concept of context-free grammar (CFG)-based coding is extended to the case of countable-context models, yielding context-dependent grammar (CDG)-based coding. Given a countable-context model, a greedy CDG transform is proposed. Based on this greedy C...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 49; no. 11; pp. 2874 - 2894
Main Authors: Yang, En-hui, He, Da-ke
Format: Journal Article
Language:English
Published: IEEE 01.11.2003
Subjects:
Algorithms
Arithmetic
Asymptotic properties
Context modeling
Councils
Data compression
Encoding
Entropy
Grammars
Greedy algorithms
Information technology
Lossless
Mathematical analysis
Pattern matching
Technological innovation
Transforms
ISSN:0018-9448
Online Access:Get full text
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Summary:For pt. I see ibid., vol.46, p.755-88 (2000). The concept of context-free grammar (CFG)-based coding is extended to the case of countable-context models, yielding context-dependent grammar (CDG)-based coding. Given a countable-context model, a greedy CDG transform is proposed. Based on this greedy CDG transform, two universal lossless data compression algorithms, an improved sequential context-dependent algorithm and a hierarchical context-dependent algorithm, are then developed. It is shown that these algorithms are all universal in the sense that they can achieve asymptotically the entropy rate of any stationary, ergodic source with a finite alphabet. Moreover, it is proved that these algorithms' worst case redundancies among all individual sequences of length n from a finite alphabet are upper-bounded by d log log n/log n, as long as the number of distinct contexts grows with the sequence length n in the order of O(n/sup a/), where 0 < /spl alpha/ < 1 and d are positive constants. It is further shown that for some nonstationary sources, the proposed context-dependent algorithms can achieve better expected redundancies than any existing CFG-based codes, including the Lempel-Ziv (1978) algorithm, the multilevel pattern matching algorithm, and the context-free algorithms in Part I of this series of papers.
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ISSN:0018-9448
DOI:10.1109/TIT.2003.818411