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Analysis of Arithmetic Coding for Data Compression
Howard, Paul G. Vitter, Jeffrey Scott
Howard, Paul G.
Vitter, Jeffrey Scott
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Abstract
Arithmetic coding, in conjunction with a suitable probabilistic model, can pro-
vide nearly optimal data compression. In this article we analyze the e ect that
the model and the particular implementation of arithmetic coding have on the
code length obtained. Periodic scaling is often used in arithmetic coding im-
plementations to reduce time and storage requirements; it also introduces a
recency e ect which can further a ect compression. Our main contribution is
introducing the concept of weighted entropy and using it to characterize in an
elegant way the e ect that periodic scaling has on the code length. We explain
why and by how much scaling increases the code length for les with a ho-
mogeneous distribution of symbols, and we characterize the reduction in code
length due to scaling for les exhibiting locality of reference. We also give a
rigorous proof that the coding e ects of rounding scaled weights, using integer
arithmetic, and encoding end-of- le are negligible.
Description
Date
1992
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
Research Projects
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Journal Issue
Keywords
Data compression, Arithmetic coding, Algorithm analysis, Adaptive modeling
Citation
P. G. Howard and J. S. Vitter. “Analysis of Arithmetic Coding for Data Compression,” invited paper in special issue on data compression for image and text in Journal of Information Processing and Management, 28(6), 1992, 749–763. An extended abstract appears in an invited paper in Proceedings of the 1991 IEEE Data Compression Conference (DCC ’91), Snowbird, UT, April 1991, 3–12. http://dx.doi.org/10.1016/0306-4573(92)90066-9