Universal lossless data compression with side information by using a conditional MPM grammar transform

A grammar transform is a transformation that converts any data sequence to be compressed into a grammar from which the original data sequence can be fully reconstructed. In a grammar-based code, a data sequence is first converted into a grammar by a grammar transform and then losslessly encoded. Amo...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 47; no. 6; pp. 2130 - 2150
Main Authors: En-Hui Yang, Kaltchenko, A., Kieffer, J.C.
Format: Journal Article
Language:English
Published: New York IEEE 01.09.2001
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Asymptotic properties
Codes
Data compression
Entropy
Ergodic processes
Grammars
Information technology
Lossless
Theory
Transforms
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Summary:A grammar transform is a transformation that converts any data sequence to be compressed into a grammar from which the original data sequence can be fully reconstructed. In a grammar-based code, a data sequence is first converted into a grammar by a grammar transform and then losslessly encoded. Among several previously proposed grammar transforms is the multilevel pattern matching (MPM) grammar transform. In this paper, the MPM grammar transform is first extended to the case of side information known to both the encoder and decoder, yielding a conditional MPM (CMPM) grammar transform. A new simple linear-time and space complexity algorithm is then proposed to implement the MPM and CMPM grammar transforms. Based on the CMPM grammar transform, a universal lossless data compression algorithm with side information is developed, which can achieve asymptotically the conditional entropy rate of any stationary, ergodic source pair. It is shown that the algorithm's worst case redundancy/sample against the k-contest conditional empirical entropy among all individual sequences of length n is upper-bounded by c(1/logn), where c is a constant. The proposed algorithm with side information is the first in the coming family of conditional grammar-based codes, whose expected high efficiency is due to the efficiency of the corresponding unconditional codes.
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ISSN:0018-9448
1557-9654
DOI:10.1109/18.945239