On adaptive strategies for an extended family of Golomb-type codes

Off-centered, two-sided geometric distributions of the integers are often encountered in lossless image compression applications, as probabilistic models for prediction residuals. Based on a recent characterization of the family of optimal prefix codes for these distributions, which is an extension of the Golomb (1966) codes, we investigate adaptive strategies for their symbol-by-symbol prefix coding, as opposed to arithmetic coding. Our strategies allow for adaptive coding of prediction residuals at very low complexity. They provide a theoretical framework for the heuristic approximations frequently used when modifying the Golomb code, originally designed for one-sided geometric distributions of non-negative integers, so as to apply to the encoding of any integer.