Minimizing Error and VLSI Complexity in the Multiplication-Free Approximation of Arithmetic Coding

Two new algorithms for performing arithmetic coding without employing multiplication are presented. The first algorithm, suitable for an alphabet of arbitrary size, reduces the worst case normalized excess length to under 0.8% versus 1.911% for the previously known best method of Chevion et al. The second algorithm, suitable only for alphabets of less than twelve symbols allows even greater reduction in the excess code length. For the important case of the binary alphabet the worst case excess code length is reduced to less than 0.1% versus 1.1% for the method of Chevion et al. The implementation requirements of the proposed new algorithms are discussed and shown to be similar to those of the algorithm proposed by Chevion et al.