Yagi Hideki, Han Te Sun
Department of Computer and Network Engineering, The University of Electro-Communications, Tokyo 182-8585, Japan.
The National Institute of Information and Communications Technology (NICT), Tokyo 184-8795, Japan.
Entropy (Basel). 2023 Oct 19;25(10):1466. doi: 10.3390/e25101466.
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.
我们引入了可变长度（VL）源可分解性问题，其中通过对一个VL均匀随机数进行编码来逼近给定的目标概率分布，并研究了该均匀随机数的渐近最小平均长度率，即所谓的VL可分解性。我们首先以变分距离作为近似度量来分析VL可分解性。接下来，我们研究以散度作为近似度量的情况。当需要渐近精确近似时，结果表明两种近似度量下的可分解性是一致的。然后我们将分析扩展到信道可分解性的情况，其中目标分布是由于固定的一般源作为输入通过一般信道的输出分布。在信道只是恒等映射的意义下，所得到的信道可分解性的特征是完全通用的，此时它简化为源可分解性的一般公式。我们还分析了二阶VL可分解性。
