  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.
