Data Compression

How Is This Possible?

• Entire King James Bible : 4,834,757 bytes• Zip Archive Containing It: 1,339,843 bytes

More Questions

• Why does this file:

• Compress different than:

Behind The Scenes

• Compression used for:– ~50% of web traffic– Most audio/video files– Sometimes for every file on a drive

Trick 1:

• Describe the contents of this file in as few words as possible…

Trick 1:

• Run Length Encoding :– Describe repetition as:

(How many times)What to repeat

– 2000000A

RLE Examples

• ABABABABABAB6AB

• AAABBBBBAAACC3A,5B,3A,2C

• 111110010101010101(5)1,(1)0,(6)01

RLE Fail

• ABCDEF1A,1B,1C,1D,1E

RLE Fail 2

• This file doesn't just have A's:

80A,1newline,80A,1newline,80A,1newline…

Trick 2

• Same As Earlier:– Describe patterns with instructions to go back x

and copy y characters

• ABCDEFG-b7c7"Write down ABCDEFG, then go back 7 characters and copy the next 7 characters to the end of what you have"

Same As Earlier

ABCDEFG-b7c7

Same As Earlier

ABCDEFG-b7c7

ABCDEFG

Same As Earlier

ABCDEFG-b7c7

ABCDEFG

Same As Earlier

ABCDEFG-b7c7

ABCDEFGA

Same As Earlier

ABCDEFG-b7c7

ABCDEFGAB

Same As Earlier

ABCDEFG-b7c7

ABCDEFGABC

Same As Earlier

ABCDEFG-b7c7

ABCDEFGABCD

Same As Earlier

ABCDEFG-b7c7

ABCDEFGABCDE

Same As Earlier

ABCDEFG-b7c7

ABCDEFGABCDEF

Same As Earlier

ABCDEFG-b7c7

ABCDEFGABCDEFG

Same As Earlier

ABCDEFG-b7c7

ABCDEFGABCDEFG

Same As Earlier

AB-b2c6

Same As Earlier

AB-b2c6

AB

Same As Earlier

AB-b2c6

AB

Same As Earlier

AB-b2c6

ABA

Same As Earlier

AB-b2c6

ABAB

Same As Earlier

AB-b2c6

ABABA

Same As Earlier

AB-b2c6

ABABAB

Same As Earlier

AB-b2c6

ABABABA

Same As Earlier

AB-b2c6

ABABABAB

Same As Earlier

AB-b2c6

ABABABAB

Same As Earlier

AB-b2c2-C-b3c4

Same As Earlier

AB-b2c2-C-b2c5

AB

Same As Earlier

AB-b2c2-C-b2c5

AB

Same As Earlier

AB-b2c2-C-b2c5

ABAB

Same As Earlier

AB-b2c2-C-b2c5

ABAB

Same As Earlier

AB-b2c2-C-b2c5

ABABC

Same As Earlier

AB-b2c2-C-b2c5

ABABC

Same As Earlier

AB-b2c2-C-b2c5

ABABCB

Same As Earlier

AB-b2c2-C-b2c5

ABABCBC

Same As Earlier

AB-b2c2-C-b2c5

ABABCBCB

Same As Earlier

AB-b2c2-C-b2c5

ABABCBCBC

Same As Earlier

AB-b2c2-C-b2c5

ABABCBCBCB

Same As Earlier

AB-b2c2-C-b2c5

ABABCBCBCB

Shorter Symbol Trick

• Normally text is 8-bit ASCII– 8bits = 256 possibilities

DEC BIN Symbol

65 01000001 A

66 01000010 B

67 01000011 C

68 01000100 D

69 01000101 E

DEC BIN Symbol

65 01000001 A

66 01000010 B

67 01000011 C

68 01000100 D

69 01000101 E

Shorter Symbol Trick

• If messages is just A's and B's we are wasting space:

A B A B

01000001 01000010 01000001 01000010

Why not:

0 1 0 1

Shorter Symbol Trick

• Shorter Symbol Trick:– Use minimum number of bits to represent

different symbols in message– More common symbols get shorter representation

More Common

• This message:

AAAABAAC

• Three symbols, need 2 bits– Could do

AAAABAAC

00 00 00 00 01 00 00 11 (16 bits)

Symbol Code

A 00

B 01

C 11

More Common

• But A is more common:

AAAABAAC

• So maybe we can use a shortercode for it

AAAABAAC

0 0 0 0 10 0 0 11 (10 bits)

Symbol Code

A 0

B 10

C 11

Why Does it Work

• No code is a prefix for another– 0 : it is an A– 1 : keep going

010110010

010110010

ABCAAB

Symbol Code

A 0

B 10

C 11

Why Does it Work

• A BAD code – 0 : is it an A?

is it the start of a D?

010 010

010 010

AB DA

Symbol Code

A 0

B 10

C 11

D 01

Building a Code

• CS160 Reader…– Huffman Code Building

Lossy Compression

• Lossless compression :– Can recreate original perfectly– Algorithms: Run length encoding, same as earlier,

shorter symbol– Examples: zip files, www traffic

Lossy Compression

• Lossy compression– Original can NOT be recreated perfectly

• My Kids - 1278Kb

• Every Other Line/Column Removed

• Remaining pixels packed back down : 320Kb

• Blown back up vs original

Original Compressed

• Only keep every 4th line/column : 81 Kb

Real JPEG

• Image broken into blocks of pixels

Real JPEG

• Each block processed seperately

Real JPEG

• Block processed, to look for compressible patterns

Real JPEG

• Patterns can more or less recreate image

JPEG Samples@ 200%

No compress Low compress Med compress High compress