Summary

DescriptionHuffman coding example.svg	The picture is an example of Huffman coding. Colors make it clearer, but they are not necessary to understand it (according to Wikipedia's guidelines): probability is shown in red, binary code is shown in blue inside a yellow frame. For a more detailed description see below (I couldn't insert a table here).
Date	18 May 2007
Source	self-made   This W3C-unspecified vector image was created with Inkscape .
Author	Alessio Damato

Description: Assume you have a source generating 4 different symbols ${\displaystyle \{a_{1},a_{2},a_{3},a_{4}\}}$ with probability ${\displaystyle \{0.4;0.35;0.2;0.05\}}$. Generate a binary tree from left to right taking the two least probable symbols and putting them together to form another equivalent symbol having a probability that equals the sum of the two symbols. Keep on doing this until you have just one symbol. Then read the tree backwards, from right to left, assigning different bits to different branches. The final Huffman code is:

The standard way to represent a signal made of 4 symbols is by using 2 bits/symbol, but the entropy of the source is 1.73 bits/symbol. If this Huffman code is used to represent the signal, then the entropy is lowered to 1.83 bits/symbol; it is still far from the theoretical limit because the probabilities of the symbols are different from negative powers of two.

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