The Optimal Compression Rate of Variable-to-Fixed Length Source Coding with a Non-Vanishing Excess-Distortion Probability

TL;DR

This paper determines the optimal compression rate for variable-to-fixed length lossy source coding with a non-zero excess-distortion probability, showing it equals (1-ε) times the rate-distortion function, aligning with fixed-to-variable length coding results.

Contribution

It establishes the first-order optimal compression rate for variable-to-fixed length source coding allowing a non-vanishing excess-distortion probability, revealing its equivalence to fixed-to-variable length coding.

Findings

Optimal rate is (1-ε)R(D) for variable-to-fixed coding.

Variable-to-fixed and fixed-to-variable coding share the same first-order rate.

Results extend understanding of lossy source coding with non-vanishing error probability.

Abstract

We consider the variable-to-fixed length lossy source coding (VFSC) problem. The optimal compression rate of the average length of variable-to-fixed source coding, allowing a non-vanishing probability of excess-distortion $\varepsilon$, is shown to be equal to $(1-\varepsilon)R(D)$, where $R(D)$ is the rate-distortion function of the source. In comparison to the related results of Koga and Yamamoto as well as Kostina, Polyanskiy, and Verd\'{u} for fixed-to-variable length source coding, our results demonstrate an interesting feature that variable-to-fixed length source coding has the same first-order compression rate as fixed-to-variable length source coding.