几乎无损模拟压缩的新一致界
New Uniform Bounds for Almost Lossless Analog Compression
摘要：
Wu和Verdú开发了一种几乎无损的模拟压缩理论，其中一个对压缩器和解压缩器施加各种规则性条件，输入信号由（通常是无限熵）平稳随机过程建模。在这项工作中，我们考虑所有平稳随机过程的轨迹在一个规定的一组$\mathcal{S} \subset [0,1]^\mathbb{Z}$的（双）无穷序列，并找到统一的下限和上界的某些压缩率的度量平均维数和平均盒维数。一个重要的工具是最近的Lindenstrauss-Tsukamoto变分原理表示度量平均维数的率失真函数。
英文摘要：
Wu and Verdú developed a theory of almost lossless analog compression, where one imposes various regularity conditions on the compressor and the decompressor with the input signal being modelled by a (typically infinite-entropy) stationary stochastic process. In this work we consider all stationary stochastic processes with trajectories in a prescribed set $\mathcal{S} \subset [0,1]^\mathbb{Z}$ of (bi)infinite sequences and find uniform lower and upper bounds for certain compression rates in terms of metric mean dimension and mean box dimension. An essential tool is the recent Lindenstrauss-Tsukamoto variational principle expressing metric mean dimension in terms of rate-distortion functions.
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