Encoding

1
Encoding

• How is information represented?

2
Way of looking at techniques
Data
Analog
Digital
Medium
NRZ Manchester Differential Manchester
Phase Coded Modulation (digitized voice)
Digital
ASK FSK PSK
AM/FM radio Television
Analog
modems
3
Analog vs Digital
Figure 3.1
Edges are crisper on digital. Attempt to store
discrete vs continuous waveforms. Some
information is more naturally analog. Some is
digital.
4
Analog

• Light waves
• Sound waves
• natural
• am fm radio
• Most waves in nature
• Waves are categorized according to frequency

5
Digital

• Most digital information derives from computer
  representation.
• Examples
• programs
• data
• Memories force representation to be digital
  because they store information digitally
• in one of two states

DIGITAL and ANALOG are not really that different!
6
Digital Data onDigital Signal
NRZ -gt 1 is low, 0 is high
T, duration of 1 bit
high value
Time
low value
1 0 1 0 0 1
1 0
Figure 3.2 NRZ Encoding
7
Beginning and End of a bit
If the values are not changing, how can the bit
times be determined?
8
Adding Timing to the Info
Manchester -gt Downward middle 0, Upward middle
1
What general observation can you make about the
bandwidth cost?
9
Another Digital encoding
Differential Manchester -gt No change at beginning
1 Change at beginning 0
10
Remember

• More timing is essential
• Costs bandwidth
• Leaves less room for data

11
Analog Data on Digital Signal

• Phone system was analog (lines and switches)
• Computers led to digital lines and switches
• Most lines still analog to end-office
• Most phones analog

lines
lines
Phone
End Office
End Office
Phone
12
How to convert?
Fig 3.12
13
Pulse Code Modulation

• Take samples
• Encode as digital values
• At receiver, use digital samples to convert back
  to analog.
• Sources of ERROR
• Number of samples
• Precision of samples

14
Process of PCM
3.17
3.18
Reverse upon reception!
15
Too few samples
Fig 3.19
Signal changes too fast. Intuition tells you to
sample more often. How fast?
16
Familiar Examples
Three points make a parabola.. Less.. Not
enough More .. Redundant
Two points make a line. Less.. Not enough More ..
Redundant
17
How about a sine wave?

• Twice as fast as the frequency of the wave
• Actually the highest frequency component
• 20-20000Hz -gt sample at 40000 Hz
• Called the Nyquist rate
• Sampling too fast is a waste!

18
Accuracy

• Number of levels dictates number of bits
• 8 levels -gt 3 bits
• 256 levels -gt 8 bits
• Too few levels -gt lose accuracy reconstructing.
• Consider a simple case of TWO levels.
• Cant have too many, but can only afford a
  limited amount!

19
CD sound application
44.1 Khz 16 bit linear
About 44000 samples / sec or 22000 Hz
signal Range of hearing about 20Khz 16 bits
generates 216 levels or 64000 levels Each
sample is accurate to one part in 64000. A
function of personal taste.
44000 samples x 2 Bytes 88K Bytes per sec 60
secs requires 60 x 88K 5280 K Bytes or 5.3 M
Bytes
20
Analog Data on Analog Signal

• Before the digital/computer age
• Dying
• Still used in tv, radio, cable tv, etc
• Carrier signal carries the information

Carrier frequency
Radio Signal 1000Hz
900
1260
1340
S(f)
Band 3
Band 1
Band 2
f
1110-1210
1290-1390
850-950
21
Figure 3.15

• Information -gt SLOWEST frequency
• Carrier -gt HIGHEST frequency
• Review previous example
• Think about your radio station
• YOU ONLY HEAR UP TO 20000 Hz
• Channel is much higher frequency for AM and
  higher yet for FM
• Not perfect example. But correct idea.

22
Digital Data on Analog Signal

• Modems
• Telephone line to the house is analog but
  information in the computer is digital.
• Lots of progressively complicated techniques in
  this section.

23
Back to Amplitude Frequency and Phase

• Encoding is change
• Encode 0 or 1 with a change in one or more of the
  basic wave features
• Some techniques can squeeze more information
  into the signal by using combinations.

24
Frequency Shift Key
Fig 3.13
0
0
1
0
1
Frequency (FSK)
25
Amplitude Shift Key
Typically have many cycles per bit time.
1
1
0
0
SameFrequency. Different Amplitudes.
26
Phase Shift Key
1
0
0
0
Phase change
27
How many bits per change?

• Two amplitudes -gt 0 or 1 -gt 1 bit
• Four amplitudes -gt 00, 01, 10, 11 -gt 2 bits
• Eight amplitudes -gt 000, 111 -gt 3 bits
• How far can you go?
• Forever as long as you have no noise and the
  sender can control with that resolution and the
  receiver can distinguish those small differences.
  Of course there is always noise!

28
Baud vs Bit Rate example
3.14
Four levels -gt 2 bits per change If this is ONE
second, bit rate is 8 bps Baud rate is 4 per
second (changes per second)
29
ASK and PSK in Combination
3.15
2 amplitudes, 4 phases -gt 8 combinations 8
combinations -gt 3 bits per change.
30
What is the ultimate limit?

• Noise
• Shannons theorem tells theoretically how far
  you can go based on noise.
• In practice even that is not achieved.
• Compression is another technique that adds the
  illusion of stretching this technique but it is
  actually an orthogonal (independent) issue.

31
How is noise measured?Relative to the signal
ratio
Signal to noise. E.g. 1000 to 1
EQUIVALENTLY and more commonly
in decibels
32
Shannons result
Where b is the bandwidth
Example -gt 20Khz medium with 30db signal to
noise MaxBitRate 20000 log2(11000)
(about) 20000 9.7
194,000 bps
33
Bandwidth vs Noise

• As bandwidth goes up, bit width becomes smaller
• As bit width becomes smaller, edges become more
  critical for proper signal interpretation
• Noise makes edges fuzzy and makes it more
  difficult to distinguish levels