Consider a lexicon of grapheme subwords G and phoneme subwords P that is extracted from a dictionary of word-pronunciation pairs, along with a joint probability distribution over G and P. As stated earlier, our objective is to minimize the entropy of phoneme subwords conditioned on a given grapheme subword, as well as the entropy of the grapheme subwords.
we would like to minimize H(P|G) + H(G), which is This objective can be restated as minimizing the expected description length of the lexicon, which is given by its entropy.