Variable-length lossy compression and channel coding: Non-asymptotic converses via cumulant generating functions

This paper gives non-asymptotic converse bounds on the cumulant generating function of the encoded lengths in variable-rate lossy compression and in variable-to-fixed channel coding. The results are given in terms of the Rényi mutual information and the d-tilted Rényi entropy. We also illustrate the application of the non-asymptotic bounds to obtain strong converses.