Analysis of Arithmetic Coding for Data Compression
Howard, Paul G.
Vitter, Jeffrey Scott
Scholarly/refereed, author accepted manuscript
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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.
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
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