Basic concepts of information theory
Before understanding shannon brown's contribution, let's understand the basic concepts of information theory.
The core concept of information theory is information entropy, which is a measure of information quantity. The greater the information entropy, the higher the uncertainty of information, and more information is needed to describe it. The formula of information entropy is:
h =-σp(x)log2p(x)
Where p(x) is the probability of occurrence of event X, and the unit of information entropy is bits, indicating the amount of information.
In addition to information entropy, information theory also involves concepts such as channel capacity and coding theory. Channel capacity refers to the maximum amount of information that a channel can transmit under a certain signal-to-noise ratio. Coding theory is to study how to encode information so that it can be transmitted more reliably in the transmission process.
Shannon brown's contribution
Shannon brown has made great contributions to the development of information theory. He put forward the concept of Shannon entropy, which is one of the core concepts of information theory. He also proposed Shannon coding, which is a lossless compression algorithm that can compress information to the minimum. The realization of Shannon coding depends on the concept of Shannon entropy, which is a probability-based coding method and can compress information lossless.
In addition, shannon brown also put forward the channel coding theorem, which shows that there is a coding method that can make the bit error rate of information transmission approach zero under a certain signal-to-noise ratio. This is of great significance to the development of digital communication and provides a theoretical guarantee for the reliability of digital communication.
Implementation of Shannon coding
The realization of Shannon coding depends on the concept of Shannon entropy, which can compress information lossless. Let's take a look at the implementation steps of Shannon coding.
1. Statistical character frequency
First of all, we need to count the frequency at which characters are encoded, that is, the probability that each character appears. For example, for the string "helloworld", the probability of the character "L" appearing is 2/ 1 1.
2. Construct Huffman Tree
Constructing Huffman tree according to character frequency. Huffman tree is a binary tree, and its leaf nodes correspond to characters, while non-leaf nodes correspond to combinations of characters. The process of constructing Huffman tree is to sort the character frequencies from small to large, and then merge the two smallest frequencies into a node until a tree is finally formed.
3. Assign codes
From the root node of Huffman tree, 0 to the left and 1 to the right, assign a code to each character. For example, the character "L" moves one step to the left and one step to the right in the Huffman tree, and the code is "10".
encode
Encode the string to be encoded. For example, for the character string "helloworld", the encoding result is "1001kloc-0/10165438".