arXiv 1907.047132019-07cs.ITmath.IT

熵与压缩：一个Khinchin-Ornstein-Shields不等式的简单证明

Entropy and Compression: A simple proof of an inequality of Khinchin-Ornstein-Shields

Riccardo Aragona, Francesca Marzi, Filippo Mignosi, Matteo Spezialetti

备注：: Compared to version 1, in version 2 we added a simpler proof than the one given by Shields of a more general theorem (Theorem 4, pg. 7) presented by Ornstein and Shields. Consequently we also modified the title of the paper. In version 3 we have reordered the sections of the paper, simplified the proof of Theorem 4 (now Theorem 3) and significantly reduced the proof of Theorem 3 (now Theorem 4)
发表信息：: Problems of Information Transmission, Vo.l 56 No. 1, 2020. A view-only published version here: https://rdcu.be/b3Cco
DOI：: 10.1134/S0032946020010020

摘要：

这篇论文关注的是民间说法“熵是压缩的下限”。更确切地说，我们来自熵定理的一个简单的证明逐点不等式首先由奥恩斯坦和希尔兹，这是几乎肯定的版本平均不等式首先由欣钦在1953年。我们进一步给出了原始Khinchin不等式的初步证明，可用作信息论学生的练习，最后给出了此类不等式的历史和技术注释。

英文摘要：

This paper concerns the folklore statement that ``entropy is a lower bound for compression''. More precisely we derive from the entropy theorem a simple proof of a pointwise inequality firstly stated by Ornstein and Shields and which is the almost-sure version of an average inequality firstly stated by Khinchin in 1953. We further give an elementary proof of original Khinchin inequality that can be used as an exercise for Information Theory students and we conclude by giving historical and technical notes of such inequality.

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