基于非顺序递归对替换的数据压缩和熵估计
Data Compression and Entropy Estimates by Non-sequential Recursive Pair Substitution
摘要：
我们认为，Jiménez-Montaño和Ebeling提出的非顺序递归对替换（NSRPS）确实可以用作最佳数据压缩算法的基础。特别是，我们证明了马尔可夫序列的NSRPS加上适当的编码的替代和替代系列不会导致代码长度的增加，在无限序列长度的限制。当应用于书面英语时，NSRPS给出的熵估计与通过其他方法获得的熵估计非常接近。使用约135 GB的输入数据，我们估计有效熵为$\approx 1.82$位/字符。外推到无限长的输入，熵的真实值估计为$\approx 0.8$位/字符。
英文摘要：
We argue that Non-sequential Recursive Pair Substitution (NSRPS) as suggested by Jiménez-Montaño and Ebeling can indeed be used as a basis for an optimal data compression algorithm. In particular, we prove for Markov sequences that NSRPS together with suitable codings of the substitutions and of the substitute series does not lead to a code length increase, in the limit of infinite sequence length. When applied to written English, NSRPS gives entropy estimates which are very close to those obtained by other methods. Using ca. 135 GB of input data from the project Gutenberg, we estimate the effective entropy to be $\approx 1.82$ bit/character. Extrapolating to infinitely long input, the true value of the entropy is estimated as $\approx 0.8$ bit/character.
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