Huffman Coding

Huffman Coding Vida Movahedi October 2006

Contents ,[object Object],[object Object],[object Object],[object Object]

A simple example ,[object Object],[object Object],[object Object],[object Object],[object Object]

A simple example – cont. ,[object Object],[object Object],[object Object],[object Object],[object Object]

Definitions ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],i a i p i h(p i ) 1 a .0575 4.1 2 b .0128 6.3 3 c .0263 5.2 .. .. .. 26 z .0007 10.4

Source Coding Theorem ,[object Object],[object Object],[object Object]

Symbol Codes ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Example ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],4 0001 d 4 0010 c 4 0100 b 4 1000 a l i c(a i ) a i C 0 :

Any encoded string must have a unique decoding ,[object Object]

The symbol code must be easy to decode ,[object Object],[object Object],[object Object],[object Object]

The code should achieve as much compression as possible ,[object Object]

Example ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],3 111 d 3 110 c 2 10 b 1 0 a l i c(a i ) a i C 1 :

The Huffman Coding algorithm- History ,[object Object],[object Object],[object Object],[object Object]

Huffman Coding Algorithm ,[object Object],[object Object],[object Object]

Example ,[object Object],[object Object],d 0.15 e 0.15 b 0.25 c 0.2 a 0.25 00 10 11 010 011 0.3 0 1 0.45 0 1 0.55 0 1 1.0 0 1

Statements ,[object Object],[object Object],[object Object]

Disadvantages of the Huffman Code ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Variations ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Image Compression ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

DPCM Differential Pulse Code Modulation ,[object Object],[object Object]

Huffman Coding Algorithm for Image Compression ,[object Object],[object Object],[object Object]

Huffman Coding of the most-likely magnitude MLM Method ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

References ,[object Object],[object Object],[object Object],[object Object]

Huffman Coding

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Huffman Coding