Cumulant Generating Function of Codeword Lengths in Variable-Length Lossy Compression Allowing Positive Excess Distortion Probability
Information Theory
2023-12-29 v2 math.IT
Abstract
This paper considers the problem of variable-length lossy source coding. The performance criteria are the excess distortion probability and the cumulant generating function of codeword lengths. We derive a non-asymptotic fundamental limit of the cumulant generating function of codeword lengths allowing positive excess distortion probability. It is shown that the achievability and converse bounds are characterized by the R\'enyi entropy-based quantity. In the proof of the achievability result, the explicit code construction is provided. Further, we investigate an asymptotic single-letter characterization of the fundamental limit for a stationary memoryless source.
Cite
@article{arxiv.1801.02496,
title = {Cumulant Generating Function of Codeword Lengths in Variable-Length Lossy Compression Allowing Positive Excess Distortion Probability},
author = {Shota Saito and Toshiyasu Matsushima},
journal= {arXiv preprint arXiv:1801.02496},
year = {2023}
}
Comments
arXiv admin note: text overlap with arXiv:1701.01800