Non-asymptotic bounds for fixed-length lossy compression

In this paper, we deal with the fixed-length lossy compression with the ε-fidelity criterion which is a kind of the distortion criterion such that the probability of exceeding a given distortion level is less than a given probability level. We give an achievability bound and a converse bound of the minimum number of codewords with this criterion. We show that our converse bound is tighter than that of Kostina and Verdú. We also show a numerical example which demonstrates that there exists some cases where our achievability bound is tighter than that of Kostina and Verdú.