On the inadequacy of Golomb-Rice codes for adaptive coding

Summary form only given. Complex data sources, like images and audio, require sophisticated coding contexts and source modeling. Fortunately, in many cases the high cost for estimating a very large number of conditional probabilities and then computing optimal codes, can be avoided by storing sets of codewords, and selecting the best choice based on local source estimates. Golomb-Rice prefix codes are commonly used for such purposes because of their convenient features. We consider the fact that, even when the source distribution is geometric, the Golomb-Rice codes are truly optimal only when the source parameter, ρ, is known with certainty, which in practice is never the case. We investigate how these codes perform - on sources with geometric distribution - depending on how ρ is estimated from previous samples. We analyze possible changes in the code to increase robustness, but keeping the useful structural properties. The intention is not to propose a "new" type of code for particular applications, but to observe how the optimal codes change with different models of source uncertainty and estimation methods. Numerical results show that the optimal codes are, as expected, always better than Golomb-Rice codes.