In this paper we present the B-coder, an efficient binary arithmetic coder that performs extremely well on a wide range of data. The B-coder should be classed as an `approximate’ arithmetic coder, because of its use of an approximation to multiplication. We show that the approximation used in the B-coder has an efficiency cost of 0.003 compared to Shannon entropy. At the heart of the B-coder is an efficient state machine that adapts rapidly to the data to be coded. The adaptation is achieved by allowing a fixed table of transitions and probabilities to change within a given tolerance. The combination of the two techniques gives a coder that out-performs the current state-of-the-art binary arithmetic coders
