Variable-length coding with epsilon-fidelity criteria for general sources

This paper addresses two problems of variablelength coding with a fidelity criterion for general sources, in which either the probability of codeword length overflow or that of excess distortion for a given threshold is allowed up to ε. In each problem, a general formula for the achievable region of coding rates and distortion levels is established via information spectrum methods. It is shown that there is a tight connection between the two problems, and the achievable regions are the same under a mild condition on the distortion measure. As a consequence, it turns out that superficially different general formulas for the two coding problems coincide with each other.