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

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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… Click to show full abstract

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.

Keywords: non asymptotic; cumulant generating; codeword lengths; function codeword; generating function

Journal Title: IEEE Transactions on Information Theory
Year Published: 2023

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