Piecewise integer mapping for arithmetic coding

By asking afresh exactly what it is the arithmetic coder must do, we show how much of the complexity of current coders can be dispensed with. In particular, we eliminate all multiplicative operations in both the encoder and decoder, replacing them by comparisons and additions. The essence of the proposal is a simple piecewise integer mapping. Graf (1997) has made use of a similar integer mapping in his proposal for a fast entropy coder. Our work is related to but independent of his. As in all non-exact coders, some inefficiency is introduced. We give an analysis that shows the average loss caused by the revised coder to be bounded in an expected sense by 0.0861 bits per symbol, which for most compression applications is just one or two percent. As an additional modification, we discuss a mechanism that allows multi-bit output of codewords without compromising the precision of the probability estimates that may be employed. Finally, we give performance results that show that in combination the two improvements yield a coder as much as 40% faster than previous benchmark arithmetic coders