如何计算位串的近似熵？ [英] How do I compute the approximate entropy of a bit string?

问题描述

Googling - 近似熵位 - 揭示了多篇学术论文，但我想要找到一个大量的伪代码来定义一个给定的任意长度的位串。

（如果这比说起来容易，而且取决于应用程序，我的应用程序涉及16,320位加密数据（cyphertext）。但加密作为一个难题，并不意味着不可能破解，我以为我会先检查熵，但不能轻易地找到一个很好的定义，所以这似乎是一个问题，应该在StackOverflow！想法从哪里开始dekyphering 16k随机看似的位也欢迎...）

另请参见相关问题：

什么是熵的计算机科学定义？

解决方案

我相信答案是 Kolmogorov复杂性的字符串。
Kolmogorov复杂性不仅仅是一大块伪代码，而是一个可计算函数< a>！

在实践中你可以做的一件事是使用最好的数据压缩算法。
压缩的熵越低。

Is there a standard way to do this?

Googling -- "approximate entropy" bits -- uncovers multiple academic papers but I'd like to just find a chunk of pseudocode defining the approximate entropy for a given bit string of arbitrary length.

(In case this is easier said than done and it depends on the application, my application involves 16,320 bits of encrypted data (cyphertext). But encrypted as a puzzle and not meant to be impossible to crack. I thought I'd first check the entropy but couldn't easily find a good definition of such. So it seemed like a question that ought to be on StackOverflow! Ideas for where to begin with de-cyphering 16k random-seeming bits are also welcome...)

See also this related question:
What is the computer science definition of entropy?

解决方案

I believe the answer is the Kolmogorov Complexity of the string. Not only is this not answerable with a chunk of pseudocode, Kolmogorov complexity is not a computable function!

One thing you can do in practice is compress the bit string with the best available data compression algorithm. The more it compresses the lower the entropy.

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