Prediction and evaluation of zero order entropy changes in grammar-based codes

Abstract

The change of zero order entropy is studied over different strategies of grammar production rule selection. The two major rules are distinguished: transformations leaving the message size intact and substitution functions changing the message size. Relations for zero order entropy changes were derived for both cases and conditions under which the entropy decreases were described. In this article, several different greedy strategies reducing zero order entropy, as well as message sizes are summarized, and the new strategy MinEnt is proposed. The resulting evolution of the zero order entropy is compared with a strategy of selecting the most frequent digram used in the Re-Pair algorithm.