String LZ77压缩算法_String_Algorithm_Math_Compression

String LZ77压缩算法

string algorithm math compression

String LZ77压缩算法,string,algorithm,math,compression,String,Algorithm,Math,Compression,我想弄清楚如何证明Lempel-ZIV 77压缩算法确实提供了最佳压缩我发现了以下信息： So how well does the Lempel-Ziv algorithm work? In these notes, we’ll calculate two quantities. First, how well it works in the worst case, and second, how well it works in the random case where each lett

我想弄清楚如何证明Lempel-ZIV 77压缩算法确实提供了最佳压缩

我发现了以下信息：

So how well does the Lempel-Ziv algorithm work? In these notes, we’ll
calculate two quantities. First, how well it works in the worst case, and
second, how well it works in the random case where each letter of the message
is chosen uniformly and independently from a probability distribution, where
the ith letter appears with probability pi
. In both cases, the compression
is asymptotically optimal. That is, in the worst case, the length of the
encoded string of bits is n + o(n). Since there is no way to compress all
length-n strings to fewer than n bits, this can be counted as asymptotically
optimal. In the second case, the source is compressed to length
                                 α
H(p1, p2, . . . , pα)n + o(n) = n∑(-pi log2 pi) + O(n)
                                     i=1
which is to first order the Shannon bound.

这里是什么意思？为什么没有办法将alllength-n字符串压缩到少于n位

谢谢大家。

有2^n个长度为n的随机字符串。为了对它们进行解压缩，压缩算法必须将它们全部压缩到不同的压缩版本：如果两个不同的n长字符串压缩到同一序列，则无法判断要将它们解压缩到哪一个。如果所有压缩到长度为k

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