A method for substituting interpolated values for ambiguous symbols in an arithmetically encoded symbol string, symbols in the unencoded original string being drawn from a Markov source and a finite alphabet. Ambiguity of a symbol is defined as where its symbol occurrence statistic lies outside of a predetermined range. Interpolation involves selectively combining the occurrence statistics of symbols adjacent the ambiguous symbol and recursively and arithmetically encoding the combined statistics. The method otherwise encode unambiguous symbols in a conventional arithmetic manner. The decoding dual are also described.