A measure of compression gain for new symbols in data-compression

Abstract

Huffman encoding is often improved by using block codes, for example a 3-block would be an alphabet consisting of each possible combination of three characters. We take the approach of starting with a base alphabet and expanding it to include frequently occurring aggregates of symbols. We prove that the change in compressed message length by the introduction of a new aggregate symbol can be expressed as the difference of two entropies, dependent only on the probabilities and length of the introduced symbol. The expression is independent of the probability of all other symbols in the alphabet. This measure of information gain, for a new symbol, can be applied in data compression methods. We also demonstrate that aggregate symbol alphabets, as opposed to mutually exclusive alphabets have the potential to provide good levels of compression, with a simple experiment. Finally, compression gain as defined in this paper may also be useful for feature selection.