Non-Asymptotic Bounds of Cumulant Generating Function of Codeword Lengths in Variable-Length Lossy Compression

This paper investigates the problem of variable-length source coding with the criteria of the normalized cumulant generating function of codeword lengths and the excess distortion probability. We analyze the non-asymptotic fundamental limit of the normalized cumulant generating function of codeword lengths under the constraint that the excess distortion probability is allowed up to
$\epsilon \in [0,1)$
. Our non-asymptotic achievability and converse bounds are characterized by the quantity related to the Rényi entropy.