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 e ? [0, 1). Our non-asymptotic achievability and converse bounds are characterized by the quantity related to the Renyi entropy.

Automated summary

This paper investigates variable length source coding with criteria of normalized cumulant generating function of codeword lengths and excess distortion probability. It analyzes the non-asymptotic fundamental limit of normalized cumulant generating function of codeword lengths under the constraint that excess distortion probability is allowed up to e ? [0, 1). The non-asymptotic achievability and converse bounds are characterized by the quantity related to Renyi entropy.