A comparison of enumerative and adaptive codes

The problem of noiselessly encoding a message when prior statistics are known is considered. The close relationship of arithmetic and enumerative coding for this problem is shown by computing explicit arithmetic coding probabilities for various enumerative coding examples. This enables a comparison to be made of the coding efficiency of Markov models and enumerative codes as well as a new coding scheme intermediate between the two. These codes are then extended to messages whose statistics are not known a priori. Two adaptive codes are described for this problem whose coding efficiency is upper-bounded by the extended enumerative codes. On some practical examples the adaptive codes perform significantly better than the nonadaptive ones.