Variable-Length Resolvability for General Sources and Channels

We introduce the problem of variable-length (VL) source resolvability, in which a given target probability distribution is approximated by encoding a VL uniform random number, and the asymptotically minimum average length rate of the uniform random number, called the VL resolvability, is investigate...

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Bibliographic Details
Published in:Entropy (Basel, Switzerland) Switzerland), 2023-10, Vol.25 (10), p.1466
Main Authors: Yagi, Hideki, Han, Te Sun
Format: Article
Language:English
Subjects:
Analysis
Approximation
Asymptotic properties
channel resolvability
Codes
Distribution (Probability theory)
Hypothesis testing
Information theory
Mathematical analysis
output approximation
Probability distribution
random number generation
Random numbers
Random variables
source resolvability
variable-length resolvability
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Summary:We introduce the problem of variable-length (VL) source resolvability, in which a given target probability distribution is approximated by encoding a VL uniform random number, and the asymptotically minimum average length rate of the uniform random number, called the VL resolvability, is investigated. We first analyze the VL resolvability with the variational distance as an approximation measure. Next, we investigate the case under the divergence as an approximation measure. When the asymptotically exact approximation is required, it is shown that the resolvability under two kinds of approximation measures coincides. We then extend the analysis to the case of channel resolvability, where the target distribution is the output distribution via a general channel due to a fixed general source as an input. The obtained characterization of channel resolvability is fully general in the sense that, when the channel is just an identity mapping, it reduces to general formulas for source resolvability. We also analyze the second-order VL resolvability.
ISSN:1099-4300
1099-4300
DOI:10.3390/e25101466