Text Compression Huffman Coding

Text CompressionText CompressionHuffman CodingHuffman Coding

James AdkisonJames Adkison

02/07/200802/07/2008

Assumptions / GivensAssumptions / Givens

• A bit is represented by a ‘1’ or ‘0’A bit is represented by a ‘1’ or ‘0’

• A byte is any combination of 8 bitsA byte is any combination of 8 bits

• All ASCII characters are stored in 1 All ASCII characters are stored in 1 byte, except the ‘\n’ character which byte, except the ‘\n’ character which is stored as two bytes the ‘\n’ and ‘\r’is stored as two bytes the ‘\n’ and ‘\r’

NotationNotation

• Square brackets ‘[’ ‘]’ are range Square brackets ‘[’ ‘]’ are range inclusiveinclusive

• Parenthesis ‘(’ ‘)’ are range exclusiveParenthesis ‘(’ ‘)’ are range exclusive

• Example: [0, 6) includes 0 and excludes Example: [0, 6) includes 0 and excludes 6 so the range is 0 to 5 or [0, 5]6 so the range is 0 to 5 or [0, 5]

• Traversing a Hoffman Tree to the left Traversing a Hoffman Tree to the left produces a ‘0’ bit and the right produces a ‘0’ bit and the right produces a ‘1’ bitproduces a ‘1’ bit

DefinitionsDefinitions

• Bit string: any combination of two or Bit string: any combination of two or more bitsmore bits

• Text = ASCII text = Uncompressed Text = ASCII text = Uncompressed text = Decoded texttext = Decoded text

• Encoded text = Huffman encoding = Encoded text = Huffman encoding = Compressed textCompressed text

Definitions Continued…Definitions Continued…

• Leaf Node: Has 1 parent and [0, 1) Leaf Node: Has 1 parent and [0, 1) childrenchildren

• Non-leaf Node: Has 1 parent and [1, Non-leaf Node: Has 1 parent and [1, 2] children2] children

• Root Node: Has 0 parents and [0, 2] Root Node: Has 0 parents and [0, 2] childrenchildren

Root Node Non-leaf Node Leaf Node

Binary Binary TreeTree

HuffmaHuffman Treen Tree0 1

‘000’

‘000’ ’010’

‘000’ ’010’ ‘011’

‘000’ ’010’ ‘011’ ‘101’

‘000’ ’010’ ‘011’

’11’

‘101’

‘000’ ’010’ ‘011’

’11’

‘101’

yqwteryqreytqywteweryqtwreqwewtryqwetytqrwqrtwtwqyqtwreqqywywytrwtqywqyqyewrqwyqwyrewqytqwtyrwyeqyrweytrtryytwrwqererrwtwqtretyytwtreryqqwewqywterqwyyqyqtweyqwreywqryqwreyqytqweytqweyqwreyqweyqwreyqwteryqwreyqwteryqwteryqwreyqwtreyqwtreyqwreyqwtreyqtwtryrereyqyqtwyweyrerrtqrwrwetqtrqywretqwwytqeyqwe

Input File:

HuffmaHuffman Treen Tree

‘t’

‘y’

‘e’

‘w’

‘r’ ‘q’

‘y’ : 0

‘w’ : 1

‘t’ : 00

‘e’ : 01

‘r’ : 10

‘q’ : 11

Input File:

Huffman

Encoding:

Uncompressed: 300 bytes

Compressed: 61 bytes

Compression: 79.7 percent

‘t’

‘y’

‘e’

‘w’

‘r’ ‘q’

‘y’ : 0

‘w’ : 1

‘t’ : 00

‘e’ : 01

‘r’ : 10

‘q’ : 11

Input File:

Huffman

Encoding:

Decode: 1110110000

‘t’

‘y’

‘e’

‘w’

‘r’ ‘q’

‘y’ : 0

‘w’ : 1

‘t’ : 00

‘e’ : 01

‘r’ : 10

‘q’ : 11

Input File:

Huffman

Encoding:

Decode: 1110110000

‘t’

‘y’

‘e’

‘w’

‘r’ ‘q’

‘y’ : 0

‘w’ : 1

‘t’ : 00

‘e’ : 01

‘r’ : 10

‘q’ : 11

Input File:

Huffman

Encoding:

Decode: 1110110000

11: ww

‘t’

‘y’

‘e’

‘w’

‘r’ ‘q’

‘y’ : 0

‘w’ : 1

‘t’ : 00

‘e’ : 01

‘r’ : 10

‘q’ : 11

Input File:

Huffman

Encoding:

Decode: 1110110000

111: www

111: wq

111: qw

‘t’

‘y’

‘e’

‘w’

‘r’ ‘q’

‘y’ : 0

‘w’ : 1

‘t’ : 00

‘e’ : 01

‘r’ : 10

‘q’ : 11

Input File:

Huffman

Encoding:

Decode: 1110110000

111: www

111: wq

111: qw

‘t’

‘y’

‘e’

‘w’

‘r’ ‘q’

‘y’ : 0

‘w’ : 1

‘t’ : 00

‘e’ : 01

‘r’ : 10

‘q’ : 11

Input File:

Huffman

Encoding:

Decode: 1110110000

111: www

111: wq

111: qw

‘t’

‘y’

‘e’

‘w’

‘r’ ‘q’

‘y’ : 0

‘w’ : 1

‘t’ : 00

‘e’ : 01

‘r’ : 10

‘q’ : 11

Input File:

Huffman

Encoding:

BadBadHuffmaHuffman Treen Tree

‘t’

‘y’

‘e’

‘w’

‘r’ ‘q’

‘y’ : 0

‘w’ : 1

‘t’ : 00

‘e’ : 01

‘r’ : 10

‘q’ : 11

Input File:

Huffman

Encoding:

BadBadHuffmaHuffman Treen Tree

Encode: q w e r t y

Code: 11 1 01 10 00 0

Huffman Tree ConstructionHuffman Tree Construction

Input File:

Huffman Tree Construction:Huffman Tree Construction:Process Text File & Build Array of Process Text File & Build Array of NodesNodes

Input File:

‘y’,1

Input File:

‘y’,1 ‘q’,1

Input File:

‘y’,1 ‘w’,1‘q’,1

Input File:

‘y’,1 ‘w’,1 ‘t’,1‘q’,1

Input File:

‘y’,1 ‘w’,1 ‘t’,1 ‘e’,1‘q’,1

Input File:

‘y’,1 ‘w’,1 ‘t’,1 ‘r’,1‘e’,1‘q’,1

Input File:

‘y’,2 ‘w’,1 ‘t’,1 ‘r’,1‘e’,1‘q’,1

Input File:

‘y’,57 ‘w’,58 ‘t’,40 ‘r’,47‘e’,43‘q’,55

Input File:

‘y’,57 ‘w’,58 ‘t’,40 ‘r’,47‘e’,43‘q’,55

Each distinct character onlyappears in the array once along

with the # of times it occurs

Huffman Tree Construction:Huffman Tree Construction:Sort the arraySort the array

Input File:

‘t’,40 ‘r’,47 ‘q’,55 ‘w’,58‘y’,57‘e’,43

Huffman Tree Construction:Huffman Tree Construction:Constructing the treeConstructing the tree

Input File:

‘t’,40 ‘r’,47 ‘q’,55 ‘w’,58‘y’,57‘e’,43

Input File:

‘t’,40

‘r’,47 ‘q’,55 ‘w’,58‘y’,57

‘e’,43

Input File:

‘t’,40

‘r’,47 ‘q’,55 ‘w’,58‘y’,57

‘e’,43

Input File:

‘t’,40

‘r’,47 ‘q’,55 ‘w’,58‘y’,57

‘e’,43

Input File:

‘t’,40

‘w’,58‘y’,57

‘e’,43

‘r’,47 ‘q’,55

Input File:

‘t’,40

‘w’,58‘y’,57

‘e’,43

‘r’,47 ‘q’,55

Input File:

‘t’,40

‘w’,58‘y’,57

‘e’,43

‘r’,47 ‘q’,55

Input File:

‘t’,40 ‘e’,43

‘r’,47 ‘q’,55

‘y’,57 ‘w’,58

Input File:

‘t’,40 ‘e’,43

‘r’,47 ‘q’,55

‘y’,57 ‘w’,58

Input File:

‘t’,40 ‘e’,43

‘r’,47 ‘q’,55

‘y’,57 ‘w’,58

Input File:‘t’,40 ‘e’,43

‘r’,47 ‘q’,55

‘y’,57 ‘w’,58

115185

‘r’,47 ‘q’,55

102‘y’,57 ‘w’,58

115 185

‘r’,47 ‘q’,55

102‘y’,57 ‘w’,58

115 185

Input File:

‘t’,40 ‘e’,43

‘r’,47 ‘q’,55

102‘y’,57 ‘w’,58

115 185

Input File:

‘t’,40 ‘e’,43

‘r’,47 ‘q’,55

102‘y’,57 ‘w’,58

115 185

‘y’,57

‘w’,58

‘t’,40

‘r’,47

‘e’,43 ‘q’,55

‘y’ : 00

‘w’ : 01

‘t’ : 100

‘e’ : 101

‘r’ : 110

‘q’ : 111

Input File:

Huffman

Encoding:

Compression: 67 percent

Huffman Tree:Huffman Tree:Compression ComputationCompression Computation

•NN : # of distinct characters : # of distinct characters•nnii : # of times a character at the i : # of times a character at the ithth

index occursindex occurs•bbii : # of bits used to encode a : # of bits used to encode a

character at the icharacter at the ithth index index• 8 : # of bits stored in a byte8 : # of bits stored in a byte

iii bn ‘y’,57 ‘w’,58 ‘t’,40 ‘r’,47‘e’,43‘q’,55

Compression Computation Compression Computation ExampleExample

• Produces:Produces:(57 * 2) + (55 * 3) + (58 * 2) + (40 * 3) + (43 * 3) + (47 * 3)(57 * 2) + (55 * 3) + (58 * 2) + (40 * 3) + (43 * 3) + (47 * 3)

= 98.125 -> 99 bytes= 98.125 -> 99 bytes

iii bn ‘y’,57 ‘w’,58 ‘t’,40 ‘r’,47‘e’,43‘q’,55

‘y’ : 00

‘w’ : 01

‘t’ : 100

‘e’ : 101

‘r’ : 110

‘q’ : 111

‘y’,57

‘w’,58

‘t’,40

‘r’,47

‘e’,43 ‘q’,55

‘y’ : 00

‘w’ : 01

‘t’ : 100

‘e’ : 101

‘r’ : 110

‘q’ : 111

Huffman

Encoding:

Decode: 1110110111010000

‘y’,57

‘w’,58

‘t’,40

‘r’,47

‘e’,43 ‘q’,55

‘y’ : 00

‘w’ : 01

‘t’ : 100

‘e’ : 101

‘r’ : 110

‘q’ : 111

Huffman

Encoding:

Decode: 1110110111010000

Answer:

‘y’,57

‘w’,58

‘t’,40

‘r’,47

‘e’,43 ‘q’,55

‘y’ : 00

‘w’ : 01

‘t’ : 100

‘e’ : 101

‘r’ : 110

‘q’ : 111

Huffman

Encoding:

Decode: 1110110111010000

Answer:

‘y’,57

‘w’,58

‘t’,40

‘r’,47

‘e’,43 ‘q’,55

‘y’ : 00

‘w’ : 01

‘t’ : 100

‘e’ : 101

‘r’ : 110

‘q’ : 111

Huffman

Encoding:

Decode: 1110110111010000

Answer:

‘y’,57

‘w’,58

‘t’,40

‘r’,47

‘e’,43 ‘q’,55

‘y’ : 00

‘w’ : 01

‘t’ : 100

‘e’ : 101

‘r’ : 110

‘q’ : 111

Huffman

Encoding:

Decode: 1110110111010000

Answer: q

‘y’,57

‘w’,58

‘t’,40

‘r’,47

‘e’,43 ‘q’,55

‘y’ : 00

‘w’ : 01

‘t’ : 100

‘e’ : 101

‘r’ : 110

‘q’ : 111

Huffman

Encoding:

Decode: 1110110111010000

Answer: q

‘y’,57

‘w’,58

‘t’,40

‘r’,47

‘e’,43 ‘q’,55

‘y’ : 00

‘w’ : 01

‘t’ : 100

‘e’ : 101

‘r’ : 110

‘q’ : 111

Huffman

Encoding:

Decode: 1110110111010000

Answer: q

‘y’,57

‘w’,58

‘t’,40

‘r’,47

‘e’,43 ‘q’,55

‘y’ : 00

‘w’ : 01

‘t’ : 100

‘e’ : 101

‘r’ : 110

‘q’ : 111

Huffman

Encoding:

Decode: 1110110111010000

Answer: qw

‘y’,57

‘w’,58

‘t’,40

‘r’,47

‘e’,43 ‘q’,55

‘y’ : 00

‘w’ : 01

‘t’ : 100

‘e’ : 101

‘r’ : 110

‘q’ : 111

Huffman

Encoding:

Decode: 1110110111010000

Answer: qw

‘y’,57

‘w’,58

‘t’,40

‘r’,47

‘e’,43 ‘q’,55

‘y’ : 00

‘w’ : 01

‘t’ : 100

‘e’ : 101

‘r’ : 110

‘q’ : 111

Huffman

Encoding:

Decode: 1110110111010000

Answer: qw

‘y’,57

‘w’,58

‘t’,40

‘r’,47

‘e’,43 ‘q’,55

‘y’ : 00

‘w’ : 01

‘t’ : 100

‘e’ : 101

‘r’ : 110

‘q’ : 111

Huffman

Encoding:

Decode: 1110110111010000

Answer: qw

‘y’,57

‘w’,58

‘t’,40

‘r’,47

‘e’,43 ‘q’,55

‘y’ : 00

‘w’ : 01

‘t’ : 100

‘e’ : 101

‘r’ : 110

‘q’ : 111

Huffman

Encoding:

Decode: 1110110111010000

Answer: qwe

‘y’,57

‘w’,58

‘t’,40

‘r’,47

‘e’,43 ‘q’,55

‘y’ : 00

‘w’ : 01

‘t’ : 100

‘e’ : 101

‘r’ : 110

‘q’ : 111

Huffman

Encoding:

Decode: 1110110111010000

Answer: qwe

‘y’,57

‘w’,58

‘t’,40

‘r’,47

‘e’,43 ‘q’,55

‘y’ : 00

‘w’ : 01

‘t’ : 100

‘e’ : 101

‘r’ : 110

‘q’ : 111

Huffman

Encoding:

Decode: 1110110111010000

Answer: qwe

‘y’,57

‘w’,58

‘t’,40

‘r’,47

‘e’,43 ‘q’,55

‘y’ : 00

‘w’ : 01

‘t’ : 100

‘e’ : 101

‘r’ : 110

‘q’ : 111

Huffman

Encoding:

Decode: 1110110111010000

Answer: qwe

‘y’,57

‘w’,58

‘t’,40

‘r’,47

‘e’,43 ‘q’,55

‘y’ : 00

‘w’ : 01

‘t’ : 100

‘e’ : 101

‘r’ : 110

‘q’ : 111

Huffman

Encoding:

Decode: 1110110111010000

Answer: qwer

‘y’,57

‘w’,58

‘t’,40

‘r’,47

‘e’,43 ‘q’,55

‘y’ : 00

‘w’ : 01

‘t’ : 100

‘e’ : 101

‘r’ : 110

‘q’ : 111

Huffman

Encoding:

Decode: 1110110111010000

Answer: qwer

‘y’,57

‘w’,58

‘t’,40

‘r’,47

‘e’,43 ‘q’,55

‘y’ : 00

‘w’ : 01

‘t’ : 100

‘e’ : 101

‘r’ : 110

‘q’ : 111

Huffman

Encoding:

Decode: 1110110111010000

Answer: qwer

‘y’,57

‘w’,58

‘t’,40

‘r’,47

‘e’,43 ‘q’,55

‘y’ : 00

‘w’ : 01

‘t’ : 100

‘e’ : 101

‘r’ : 110

‘q’ : 111

Huffman

Encoding:

Decode: 1110110111010000

Answer: qwer

‘y’,57

‘w’,58

‘t’,40

‘r’,47

‘e’,43 ‘q’,55

‘y’ : 00

‘w’ : 01

‘t’ : 100

‘e’ : 101

‘r’ : 110

‘q’ : 111

Huffman

Encoding:

Decode: 1110110111010000

Answer: qwert

‘y’,57

‘w’,58

‘t’,40

‘r’,47

‘e’,43 ‘q’,55

‘y’ : 00

‘w’ : 01

‘t’ : 100

‘e’ : 101

‘r’ : 110

‘q’ : 111

Huffman

Encoding:

Decode: 1110110111010000

Answer: qwert

‘y’,57

‘w’,58

‘t’,40

‘r’,47

‘e’,43 ‘q’,55

‘y’ : 00

‘w’ : 01

‘t’ : 100

‘e’ : 101

‘r’ : 110

‘q’ : 111

Huffman

Encoding:

Decode: 1110110111010000

Answer: qwert

‘y’,57

‘w’,58

‘t’,40

‘r’,47

‘e’,43 ‘q’,55

‘y’ : 00

‘w’ : 01

‘t’ : 100

‘e’ : 101

‘r’ : 110

‘q’ : 111

Huffman

Encoding:

Decode: 1110110111010000

Answer: qwerty

‘y’,57

‘w’,58

‘t’,40

‘r’,47

‘e’,43 ‘q’,55

‘y’ : 00

‘w’ : 01

‘t’ : 100

‘e’ : 101

‘r’ : 110

‘q’ : 111

Huffman

Encoding:

Decode: 1110110111010000

Answer: qwerty

Huffman EncodingHuffman EncodingReal World ExampleReal World Example

• Huffman (C++)Huffman (C++)

• Text I/O DirectoryText I/O Directory

Huffman HomeworkHuffman Homework

1.1. Construct a Huffman tree for the Construct a Huffman tree for the following input file. You only need to following input file. You only need to show the final tree. These are the only show the final tree. These are the only characters in the file and the # of times characters in the file and the # of times they occur: (a, 50)(b, 60)(c, 70)(d, 80)they occur: (a, 50)(b, 60)(c, 70)(d, 80)

2.2. How many bytes will the compressed How many bytes will the compressed text file occupy?text file occupy?

Works CitedWorks Cited

• ““ASCII.” ASCII.” Wikipedia The Free EncyclopediaWikipedia The Free Encyclopedia. 2008. . 2008. 21 January 2008. <21 January 2008. <http://http://en.wikipedia.orgen.wikipedia.org/wiki/ASCII/wiki/ASCII>>

• Dewdney, A. K. Dewdney, A. K. The New Turing OmnibusThe New Turing Omnibus. New . New York: Henry Holt, 1989. Pages 345 – 350.York: Henry Holt, 1989. Pages 345 – 350.

• Line Termination: Operating Systems Use Line Termination: Operating Systems Use Different ConventionsDifferent Conventions. 21 January 2008. <. 21 January 2008. <http://homepage.smc.edu/morgan_david/CS41/linhttp://homepage.smc.edu/morgan_david/CS41/lineterminators.htmeterminators.htm>>

Text Compression Huffman Coding

Documents

Transcript of Text Compression Huffman Coding

IMAGE COMPRESSION - EVTEKusers.evtek.fi/~erkkir/ImageTechnology2013/1 ImagetechPDF/7... · Lossless image compression • Image can be decompressed back to original ... Huffman coding

Lossless Huffman coding technique for image compression ... · PDF fileLOSSLESS HUFFMAN CODING TECHNIQUE FOR IMAGE COMPRESSION AND RECONSTRUCTION USING BINARY TREES . 1Mridul Kumar

Image Compression (in addition to notes) - BGUiip/slides/compression.pdf · Image Compression (in addition to notes) ... transform image coding (DFT, DCT, ... • Huffman coding for

3.3.8 Data compression (Huffman coding) Lesson plan and ...

03: Huffman Coding - vernier.frederic.free.frvernier.frederic.free.fr/Teaching/InfoTermS/InfoNumerique/Vassil... · 03: Huffman Coding CSCI 6990 Data Compression Vassil Roussev 15

Huffman Coding Vida Movahedi October 2006. Contents A simple example Definitions Huffman Coding Algorithm Image Compression.

The Weather-Huffman Method of Data Compression of …...HUFFMAN RUNLENGlH CODING 15 3.1 Image Scanning Procedures 15 3.2 Codeword Determination 18 3.3 Huffman Decoding Table Representation

Week 11 Image Compression - canerozcan.netcanerozcan.net/files/CME429_Week10.pdf · Image Compression But life is short ... Some Basic Compression Methods: Huffman Coding 12 The average

Fault Tolerant Huffman Coding for JPEG Image Coding System...JPEG image compression standard applies the Huffman table instead of tree structure, the fault tolerant design for this

Lecture 12: Compression & coding › ~ffh8x › d › soi19S › Lecture12.pdf · Huffman coding A Huffman code is a prefix code with a binary tree structure. It is generated on-the-fly

Compression & Huffman Codes

LOSSLESS HUFFMAN CODING FOR IMAGE COMPRESSION … · size like of 64 in the context lossless Huffman coding for image compression using K-Means algorithm and Video estimation technique

Huffman Coding

SIMS-201 Compressing Information. 2 Overview Chapter 7: Compression Introduction Entropy Huffman coding Universal coding.

UNIT II TEXT COMPRESSION. a. Outline Compression techniques Run length coding Huffman coding Adaptive Huffman Coding Arithmetic coding Shannon-Fano coding.

Data Compression Engine Enhancement Using Huffman Coding Algorithm2

Fault Tolerant Huffman Coding for JPEG Image Coding … · Fault Tolerant Huffman Coding for JPEG Image Coding System ... JPEG image compression standard applies the Huffman table

Image Compression Techniques -A revie Renu.pdf · 2019-02-28 · compression: D Area Coding 1. Run length encoding 2. Huffman encoding 3. LZW coding 4. Area coding sequences, 2 Lossy

2 Huffman Coding

Compression and Huffman Coding - University of Calgarypages.cpsc.ucalgary.ca/~marina/319/CPSC319_Compression.pdfHuffman Coding Non-determinism of the algorithm Implementations: Singly-linked