Arithmetic coding with dual symbol sets and its performance analysis

We propose a novel adaptive arithmetic coding method that uses dual symbol sets: a primary symbol set that contains all the symbols that are likely to occur in the near future and a secondary symbol set that contains all other symbols. The simplest implementation of our method assumes that symbols that have appeared in the previously are highly likely to appear in the near future. It therefore fills the primary set with symbols that have occurred in the previously. Symbols move dynamically between the two symbol sets to adapt to the local statistics of the symbol source. The proposed method works well for sources, such as images, that are characterized by large alphabets and alphabet distributions that are skewed and highly nonstationary. We analyze the performance of the proposed method and compare it to other arithmetic coding methods, both theoretically and experimentally. We show experimentally that in certain contexts, e.g., with a wavelet-based image coding scheme that has appeared in the literature, the compression performance of the proposed method is better than that of the conventional arithmetic coding method and the zero-frequency escape arithmetic coding method.