Speeding up Arithmetic Coding using Greedy Re-normalization

A typical adaptive arithmetic coder consists of three steps: range calculation, renormalization, and probability model updating. A method, called greedy re-normalization, is given in this paper that significantly reduces the computational complexity of the renormalization step of arithmetic coding. This is achieved by reducing both the number of re-normalizations required to encode a sequence and the number of operations within each re-normalization. Following the notations in [1], the internal state of an arithmetic coder is represented by an interval [L, L + R) whereL is the base of the interval and R the length, and both L and R are b-bit integers. To reduce the number of operations within each re-normalization, the greedy re-normalization method generates as many code bits as possible from an interval and updates the interval correspondingly; moreover, both of the tasks are done at one time without using a loop. This is one of the differences between the greedy re-normalization method and the conventional method in [1] where a loop is used to generate code bits and update an interval. Let m(L, R) represent the maximal number of code bits with known polarities that can be generated from [L, L + R) andk(L, R) the maximum number o