1. Computer Science 335
Data Compression

2. Compression .. Magic or Science
Only works when a MORE EFFICIENT means of encoding can be found
Special assumptions must be made about the data in many cases in order to gain compression benefits
“Compression” can lead to larger files if the data does not conform to assumptions

3. Why compress? In files on a disk In internet access
save disk space
In internet access
reduce wait time
In a general queueing system
keep paybacks can be more than linear if operation is nearing or in saturation

4. A typical queueing graph
Delay
66 %
delay
decrease
Load
25% load decrease

5. Example Ascii characters require 7 bits
Data may not use ALL characters in Ascii set
consider just digits 0..9
Only 10 values -> really only requires 4 bits
There is actually a well used code for this which also allows for +/- -> BCD

6. Other Approaches

7. Run length encoding Preface each run with a 8-bit length byte
aaabbabbbccdddaaaa -> 18 bytes
3a2b1a3b2c3d4a > 14 bytes
benefit from runs of 3 or more
aaa versus 3a
No gain or loss
aa versus 2a
lose in single characters
a versus 1a

8. Facsimile Compression (example of run-length encoding)
Example of application of run-length encoding.
Decomposed into black/white pixels
Lots of long runs of black and white pixels
Don’t encode each pixel but runs of pixels

9. Differential encoding
values between 1000 and 1050
1050 requires 11 bits
difference plus +/- requires 7 bits
6 bits -> 64
1 additional bit for direction (+/-)
Differential encoding can lead to problems as each value is relative to the last value.
Like directions, one wrong turn and everything else is irrelevant.

10. Frequency Based Encoding
Huffman
Encoding is not the same length for all values
Short codes for frequently occurring symbols
Longer codes for infrequently occurring
Arithmetic (not responsible for this)
Interpret a string as a real number
Infinite number of values between 0 and 1
Divide region up based on frequency
A ->12% and B 5%, A is 0 to 0.12 and B 0.12 to 0.17
Limit based on the fact that computer has limited precision

11. Huffman (more details)

12. Huffman encoding Must know distribution of symbols
Symbols typically have DIFFERENT lengths unlike most schemes you have seen (Ascii, etc)
Characters occurring most have shortest code
Characters occurring least have longest
Solution minimal but not unique

13. Assume following data
A -> 30%
B-> 20%
C-> 10 %
D-> 5%
E-> 35%

14. Lets peek at the answer Note that you read the encoding1
Note that you read the encoding
of a character from top to bottom.
For example C is
Also note that choice of 0 or 1
for a branch is arbitrary. 1 E A 1 B 1 C D

15. Build the solution tree Choose the smallest two at a time and group
This could choose E and A instead! A 30 B 1 65 20 1 E C 35 10 A 1
100 D 15 B 5 1 C E D 35

16. And the binary encoding..1
A 00 B C D
E 1 1 E A 1 B 1 C D

17. Compute expected length
Expected Bits
Per Character
.3*2 +
.2*3 +
.1*4 +
.05*4 +
.35*1
A 00 B C D
E 1
A -> 30%
B-> 20%
C-> 10 %
D-> 5%
E-> 35%
.6+
.4+
.2+
.35 = =
2.15
Each symbol has average length of 2.15 bits
You would have assumed 5 values -> 3 bits

18. Is it hard to interpret a message?
Message Example:
A 00 B C D
E 1
A E B A D
NOT REALLY!
What if last 1 in message was missing? -> illegal
While message is not ambiguous, illegal message are possible

19. Observations of Huffman
Method creates a shorter code
Assumes knowledge of symbol distribution
Different symbols .. Different length
Knowing distribution ahead of time is not always possible!
Another version of Huffman coding can solve that problem

20. Revisiting Facsimiles
Huffman says one can minimize by assigning different length codes to symbols
Fax transmissions can use this principle to give short messages to long runs of white/black pixels/
Run-length combined with Huffman
See Table 5.7 in the text

21. Table 5.7 Example: 66 white -> 64 + 2 = 110110111 TERMINATING
Length White Black
Example:
66 white -> =
MAKEUP
Length White Black

22. Multimedia compression
Many of these include techniques that result in “lossy” compression. Uncompressing results in loss of information.
This loss is tolerated because the inaccuracy is only perceivable based on human perception
Video
Pictures
Audio
Compression ratios of other techniques result in 2-3:1
Compression in multimedia need 10-20:1
Compression rates achieved by lossy techniques -> tradeoff
Techniques
JPEG – pictures
MPEG – motion pictures
MP3 - music

23. Image compression Represented as RGB
8 bits typical for each color
Or as Luminance (brightness 8 bits) and Chrominance (color 16 bits)
Perception of color by humans reacts significantly to light in addition to color
Really two ways to represent the same thing
Y = 0.30R G B (luminance)
I = 0.60R G – 0.32B (color)
Q = 0.21R – 0.52G B (color)

24. JPEG Image -> DCT Phase Quantization Phase Encoding Phase
Compressed
Image
->
->
->
So how does this work?

25. JPEG algorithm Consider 8x8 blocks at a time
Create 3 8x8 arrays with color values of each pixel(for RGB)
Now go through a complex transformation (theory beyond us)
When you finish the transformation the numbers in upper left
indicate little variation in color in the block, values further
away from [0,0] indicate large color variation
- see fig 5.10 top one with small variation, bottom with large
Simplify the numbers in the result (eliminate small values) by
dividing by an integer and then truncating.
see Eqn 5-5
- value is different for each term and application dependent
Use encoding (run-length) and odd pattern (Fig 5.11) to compress
I don’t expect you to do this on a test, but it shows how JPEG is lossy.

26. MPEG
Uses differential encoding to compare successive frames of a motion picture.
Three kinds of frames:
I -> JPEG complete image
P -> incremental change to I (where block moves)
½ size I
B -> use a different interpolation technique
¼ size I
Typical sequence -> I B B P B B I ….

27. MP3 Music/audio compression Uses psychoacoustic principles
Some sounds can’t be heard because they are drowned by other louder sounds (freqs)
Divide the sound into smaller subbands
Eliminate sounds you can’t hear anyway because others are too loud.
3 types with varying compression
Layer 1 4:1 192K
Layer 2 8:1 128K
Layer 3 12:1 64K