On the adaptive source coding

Abstract

We compare adaptive source coding algorithms. Description of the Huffman-Gallager algorithm can use a transition diagram were the tree leaves merge with its root. We show that the Lempel-Ziv algorithm can be used as a means for constructing a diagram of same shape. When the probability of each branch conditioned on the node it departs from is constant and known, the Guazzo algorithm is a means for describing any path in such a diagram, hence any source output. It results in a coded message whose average length approaches the theoretical limit as a closeness criterion is made arbitrarily tight. Its adaptive version replaces the conditional probabilities by frequencies. We consider its use on a diagram constructed by the Lempel-Ziv algorithm, preferably transformed by the Huffman-Gallager algorithm.