Paper Topic : Huffman coding Codes1.pdf• Paper topic: Huffman coding. Information Retrieval 902333 6 Huffman Coding • Uses the minimum number of bits • Variable length coding

Information Retrieval 902333 1

Paper Topic : Huffman Paper Topic : Huffman codingcoding

Team Members :Team Members :HanaHana’’a shdefat 0950902031a shdefat 0950902031Bushra hasaien 0900902008Bushra hasaien 0900902008

Dr.SaifDr.Saif RababahRababah


Data CompressionData Compression

•• PressurePressure data:data:data compression (for a picture or sound or video or text , or to draw a Graphics ... etc.) is to reduce the size of the data. The main aim of data compression is to reduce the file size.


Type of Data Type of Data CompressionCompression

Data compressionData compression in generalin general is dividedis divided into two into two partsparts oror two types, namely:two types, namely:

o The first type is called (Lossless) without losing anything. that the file is the output of the compression process Photocopy the original file before any pressure without losing anything.

o The second type is called (Lossy) the loss of everything .that the file output of the compression process is

similar to the original file to a certain extent, . But these data are the data lost is essential to us (for the User).


History of Huffman codes• In 1951 was Professor Robert M.. Fano (who was a

professor at the Massachusetts Institute of Technology), who teaches Trivhtermaz Shannon -Fano his students. The Professor Btejearstudents either to attend the final exam or Ajdo way better and more efficient than encoding Shannon -Fano. Try David Hoffman- and it was one of the students, Professor - to find a better way ofShannon - Fano path of trial and error and was about to give upthe idea and Alstaadad of the test until he found a way to build atree from the bottom up unlike encoding Shannon -Fano and thusthe encoding is better than coding Shannon - Fano


David A. Huffman• BS Electrical Engineering at

Ohio State University• Worked as a radar maintenance

officer for the US Navy• PhD student, Electrical

Engineering at MIT 1952• Was given the choice of writing

a term paper or to take a final exam

• Paper topic: Huffman coding


Huffman Coding

• Uses the minimum number of bits• Variable length coding – good for data transfer

– Different symbols have different lengths• Symbols with the most frequency will result

in shorter codewords• Symbols with lower frequency will have

longer codewords• “Z” will have a longer code representation

then “E” if looking at the frequency of character occurrences in an alphabet

• No codeword is a prefix for another codeword!


DecodingDecoding

• To determine the original message, read the string of bits from left to right and use the table to determine the individual symbols

ABCABCABCA

Decode the following: 01101101101101101101

SymSymbolbol

CodCodee

A 01

B 10

C 11


Decoding

Original String:Original String:01101101101101101101

Symbol

Code

A 01

B 10

C 11

10 11 01 10 1101 01 10 11 01

A A A AB B BC C C


• This text contain 10 character8 * 10 = 80 bit• To represent the text with 2

bits instead of 8-bit 2 * 10 = 20 bit• In this case is not lost from the text

but on the contrary, we reduced space

• Compression ratio = compressed text \ text non-compressed20 \ 80 = %25


• A is More than a repetition of the characters that place just put (0)

• 0101101011010110• 4A 4 * 1 • 3B 3 * 2• 3C 3 * 2• 4 + 6 + 6 = 16 bit• Compression

ratio = compressed text \ text non-compressed16 \ 80 = % 20

SymSymbolbol

CodCodee

A 0

B 10

C 11


Representing a Huffman Table as Representing a Huffman Table as a Binary Treea Binary Tree

• Codewords are presented by a binary tree• Each leaf stores a character• Each node has two children

– Left = 0– Right = 1

• The codeword is the path from the root to the leaf storing a given character

• The code is represented by the leads of the tree is the prefix code


AlgorithmAlgorithm• Make a leaf node for node symbol

– Add the generation probability for each symbol to the leaf node

• Take the two leaf nodes with the smallest probability (pi) and connect them into a new node (which becomes the parent of those nodes)– Add 1 for the right edge– Add 0 for the left edge– The probability of the new node is the sum

of the probabilities of the two connecting nodes

• If there is only one node left, the code construction is completed.


Algorithm Huffmanalgorithm Huffman (C,f){n:=|C|;Q:=C;for i:=1 to n-1 do{ z:=NewNode();x:=z.left:=GetMin(Q);y:=z.right:=GetMin(Q);f[z]:=f[x]+f[y];insert (Q,z);}return GetMin(Q);}


Example

Symbol

FrequencyA 5

B 2C 2D 1E 1


Example – Creating the tree

D 1

C 2

A5

B2

E 1

Symbol

Frequency

A 5B 2C 2D 1E 1


E

D

CBA

SymbolSymbol

1

1

225

FrequenFrequency cy

SymbolSymbol FrequenFrequency cy

A 5B 2C 2

1 2

• Green nodes – nodes to be evaluated• White nodes – nodes which have already been evaluated• Blue nodes – nodes which are added in this iteration

Take the two leaf nodes with the smallest probability (pi) and connect them into a new node (which becomes the parent of those nodes)


1. Step

D 1

C 2

A 5

B2

E 1

2

0 1


2. Step

D 1

C2

E 1

2

4

0 1

E

D

CBA

SymboSymboll

1

1

225

FrequeFrequency ncy

SymbolSymbol FrequeFrequency ncy

A 5B 22 4

10


D1

B2

E 1

2 C2

4

3. Step

10

10

6

0 1

EDCBA

Symbol

11225

Frequency

Symbol Frequency

A 53 6


Example: Completed Tree

D1

A 5

E1

B2

2

6

11

1

0

0

0

1

1

4

C2

10


Finally we convert theFinally we convert theTree to prefix codeTree to prefix code

Symbol Frequency

A 0B 10C 111D 1100E 1101

Generate the table by reading from the root node to the leaves for each symbol


Questions?Questions?


ReferencesReferences• http://www.cstutoringcenter.com/tutori

als/algorithms/huffman.php• http://en.wikipedia.org/wiki/Huffman_c

oding• http://michael.dipperstein.com/huffma

n/index.html• http://en.wikipedia.org/wiki/David_A._

Huffman• http://www.binaryessence.com/dct/en

000080.htm


Thanks AllThanks All

Documents

Paper Topic : Huffman coding Codes1.pdf• Paper topic: Huffman coding. Information Retrieval 902333 6 Huffman Coding • Uses the minimum number of bits • Variable length coding