Coding of sources with two-sided geometric distributions and unknown parameters

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. 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.