香农信源编码定理

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模板:简述

模板:Information theory 模板:信息论


模板:关于数据压缩中的源码理论


In information theory, Shannon's source coding theorem (or noiseless coding theorem) establishes the limits to possible data compression, and the operational meaning of the Shannon entropy.

In information theory, Shannon's source coding theorem (or noiseless coding theorem) establishes the limits to possible data compression, and the operational meaning of the Shannon entropy.

在信息理论中, 香农信源编码定理 Shannon's source coding theorem (或无噪声编码定理)建立了可能的 数据压缩 data compression 的极限,以及 香农熵 Shannon entropy 的操作意义。


Named after Claude Shannon, the source coding theorem shows that (in the limit, as the length of a stream of independent and identically-distributed random variable (i.i.d.) data tends to infinity) it is impossible to compress the data such that the code rate (average number of bits per symbol) is less than the Shannon entropy of the source, without it being virtually certain that information will be lost. However it is possible to get the code rate arbitrarily close to the Shannon entropy, with negligible probability of loss.

Named after Claude Shannon, the source coding theorem shows that (in the limit, as the length of a stream of independent and identically-distributed random variable (i.i.d.) data tends to infinity) it is impossible to compress the data such that the code rate (average number of bits per symbol) is less than the Shannon entropy of the source, without it being virtually certain that information will be lost. However it is possible to get the code rate arbitrarily close to the Shannon entropy, with negligible probability of loss.

以克劳德·香农 Claude Shannon命名的信源编码定理表明,(在极限情况下,当独立的均匀分布的随机变量(i.i.d.)数据流的长度趋于无穷大时)不可能压缩数据使编码率(每个符号的平均比特数)小于信源的香农熵,而事实上又不能确定信息会丢失。然而,可以任意地使码率接近香农熵,损失的概率可以忽略不计。


The source coding theorem for symbol codes places an upper and a lower bound on the minimal possible expected length of codewords as a function of the entropy of the input word (which is viewed as a random variable) and of the size of the target alphabet.

The source coding theorem for symbol codes places an upper and a lower bound on the minimal possible expected length of codewords as a function of the entropy of the input word (which is viewed as a random variable) and of the size of the target alphabet.

符号码的信源编码定理根据输入单词(被视为一个随机变量)熵和目标字母表大小将最小可能期望码字长度作为一个函数,并设置了一个上下界。


Statements

说明

Source coding is a mapping from (a sequence of) symbols from an information source to a sequence of alphabet symbols (usually bits) such that the source symbols can be exactly recovered from the binary bits (lossless source coding) or recovered within some distortion (lossy source coding). This is the concept behind data compression.

Source coding is a mapping from (a sequence of) symbols from an information source to a sequence of alphabet symbols (usually bits) such that the source symbols can be exactly recovered from the binary bits (lossless source coding) or recovered within some distortion (lossy source coding). This is the concept behind data compression.

信源编码是从信源符号序列到字母符号序列(通常是比特)的映射,使信源符号能够准确地从二进制比特位(无损源编码)恢复或在某种失真(有损源编码)范围内恢复。这就是数据压缩的概念。


Source coding theorem

信源编码定理

In information theory, the source coding theorem (Shannon 1948)[1] informally states that (MacKay 2003, pg. 81,[2] Cover 2006, Chapter 5[3]):

In information theory, the source coding theorem (Shannon 1948)

在信息论中,信源编码定理(Shannon,1948) [1]非正式地表明(MacKay 2003, pg. 81,[2] Cover 2006, Chapter 5[3]):


N i.i.d. random variables each with entropy H(X) can be compressed into more than N H(X) bits with negligible risk of information loss, as N → ∞; but conversely, if they are compressed into fewer than N H(X) bits it is virtually certain that information will be lost.

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Ni.i.d.每个随机变量都有H(X)可以压缩成超过N H(X)。随着N → ∞的信息丢失风险可以忽略不计;但反过来说,如果它们被压缩成少于N H(X)位,则信息肯定将丢失。


Source coding theorem for symbol codes

符号码的源码定理

Category:Information theory

范畴: 信息论

Let Σ1, Σ2 denote two finite alphabets and let Σ模板:Su and Σ模板:Su denote the set of all finite words from those alphabets (respectively).

Σ1, Σ2表示两个有限字母,并让Σ模板:SuΣ模板:Su分别表示这些字母中所有有限词的集合

Category:Coding theory

类别: 编码理论


Category:Data compression

类别: 数据压缩

Suppose that X is a random variable taking values in Σ1 and let f be a uniquely decodable code from Σ模板:Su to Σ模板:Su where 2| = a. Let S denote the random variable given by the length of codeword f (X).

假设X是一个随机变量,取值在Σ1,让f是一个唯一可解码代码,从Σ{su}}到Σ{su}},其中2模板:!。= a. 让S表示由码字f (X)的长度给出的随机变量。

Category:Presentation layer protocols

分类: 表示层协议


Category:Mathematical theorems in theoretical computer science

范畴: 理论计算机科学中的数学定理

If f is optimal in the sense that it has the minimal expected word length for X, then (Shannon 1948):

Category:Articles containing proofs

类别: 包含证明的文章


This page was moved from wikipedia:en:Shannon's source coding theorem. Its edit history can be viewed at 香农信源编码定理/edithistory

  1. 1.0 1.1 引用错误:无效<ref>标签;未给name属性为Shannon的引用提供文字
  2. 2.0 2.1 引用错误:无效<ref>标签;未给name属性为MacKay的引用提供文字
  3. 3.0 3.1 引用错误:无效<ref>标签;未给name属性为Cover的引用提供文字