Information spectrum approach to fixed-length lossy source coding problem with some excess distortion probability

This paper deals with a fixed-length lossy source coding problem with some excess distortion probability called the source coding problem with ε-fidelity criterion. In this problem, the rate-distortion function and the distortion-rate function have already been characterized for i.i.d. sources with an additive distortion measure in the sense of first-order and second-order coding rates. However, general formulas for these functions have not been revealed up to present. Hence, in this paper we derive general formulas for the rate-distortion function and the distortion-rate function with the ε-fidelity criterion in both of the first-order and second-order cases. A relationship between our general formulas and previous results are also discussed.