Coding of Sources with Two-Sided Geometric Distributions and Unknown Parameters ∗ Neri Merhav † Electrical Engineering Department Technion Haifa 32000, Israel Gadiel Seroussi and Marcelo J. Weinberger Hewlett-Packard Laboratories 1501 Page Mill Road Palo Alto, CA 94304, USA. Abstract Lossless compression is studied for a countably infinite alphabet source with an unknown, off-centered, two-sided geometric (TSG) distribution, which is a commonly used statistical model for image prediction residuals. In this paper, we demonstrate that arithmetic coding based on a simple strategy of model adaptation, essentially attains the theoretical lower bound to the universal coding redundancy associated with this model. We then focus on more practical codes for the TSG model, that operate on a symbol-by-symbol basis, and study the problem of adaptively selecting a code from a given discrete family. By taking advantage of the structure of the optimum Huffman tree for a known TSG distribution, which enables simple calculation of the codeword of every given source symbol, an efficient adaptive strategy is derived. Index Terms: Lossless image compression, infinite alphabet, geometric distribution, expo- nential distribution, Golomb codes, prediction residual, universal coding, sequential coding, universal modeling. ∗ Parts of this paper were presented in the 1996 International Conference on Image Processing, Lausanne, Switzerland, and in the 1997 International Symposium on Information Theory, Ulm, Germany. † This work was done while the author was on sabbatical leave at Hewlett-Packard Laboratories, Palo Alto, California. The author is also with Hewlett-Packard Laboratories—Israel in Haifa, Israel. To appear, IEEE Trans. Information Theory