Range Encoding - Relationship With Arithmetic Coding

Relationship With Arithmetic Coding

Arithmetic coding is the same as range encoding, but with the integers taken as being the numerators of fractions. These fractions have an implicit, common denominator, such that all the fractions fall in the range [0,1). Accordingly, the resulting arithmetic code is interpreted as beginning with an implicit "0.". As these are just different interpretations of the same coding methods, and as the resulting arithmetic and range codes are identical, each arithmetic coder is its corresponding range encoder, and vice-versa. In other words, arithmetic coding and range encoding are just two, slightly different ways of understanding the same thing.

In practice, though, so-called range encoders tend to be implemented pretty much as described in Martin's paper, while arithmetic coders more generally tend not to be called range encoders. An often noted feature of such range encoders is the tendency to perform renormalization a byte at a time, rather than one bit at a time (as is usually the case). In other words, range encoders tend to use bytes as encoding digits, rather than bits. While this does reduce the amount of compression that can be achieved by a very small amount, it is faster than when performing renormalization for each bit.