Digital transmission fundamentals (chap.3

1
Digital transmission fundamentals (chap.3 4)

• What is digital transmission?
• Why digital transmission?
• How to represent different information
• in digital format?
• What is Bit rate/bandwidth?
• What are the properties of different media?
• How to do error detection and correction?
• Multiplexing?

2
What is digital transmission?

• Analog transmission
• Continuous waveform
• Digital representation and transmission
• Discrete binary sequence/pulses
• 1 a rectangular pulse of amplitude 1 and of
  duration 0.125 milliseconds
• 0 a rectangular pulse of amplitude -1 and of
  duration of 0.125 milliseconds.

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Figure 3.13
4
Figure 3.14
5
Analog ?Digital ? --PCM

• Analog signal such as voice/music
• continuous waveform, i.e, variations in air
  pressure.
• Bandwidth a measure of how fast the signal
  varies, i.e., cycles/second, or Hertz.
• Two stages
• Sampling for bandwidth W, minimum sampling rate
  is 2W.
• Quantizing how many levels to represent a
  sample.
• Example W4 kHz, sampling rate8K
  samples/second. Sample period is T1/8000125
  microseconds. Suppose 8 bits/sample (256 levels),
  then PCM bit rate is 8000864 kbps.

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(a)
7D/2
5D/2
3D/2
D/2
-D/2
-3D/2
-5D/2
-7D/2
7D/2
(b)
5D/2
3D/2
D/2
-D/2
-3D/2
-5D/2
-7D/2
Figure 3.2
7
Why digital?

• For analog
• output should reproduce the input exactly. No
  distortion.
• Repeater amplifies noise, difficult task.
• Too much repeaters may make noise too large, so
  limited distance
• Cost is high.
• Basic voice/telephone service.
• For digital
• Not exact, as long as can distinguish 1 or o.
• Digital regenerator generates pure digital
  numbers, easy.
• No limitation on digital regenerators, no
  distance limitation.
• Cost is low.
• More other services, easily multiplexing, more
  functions.

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• (a) Analog transmission all details must be
  reproduced accurately

Received
Sent

• e.g. AM, FM, TV transmission

(b) Digital transmission only discrete levels
need to be reproduced
Received
Sent

• e.g digital telephone, CD Audio

Figure 3.6
9
Transmission segment
Destination
Source
Repeater
Repeater
Figure 3.7
10
Recovered signal residual noise
Attenuated distorted signal noise
Amp.
Equalizer
Repeater
Figure 3.8
11
Decision Circuit. Signal Regenerator
Amplifier Equalizer
Timing Recovery
Distorted Digital signal is easy to restore by
regenerator.
Figure 3.9
12
Digital representations for different information

• Text ASCII
• Scanned WB documents
• A4 paper, 200 X 100 pixels/inch. 256KB.
• Color pictures/images
• 8 X 10 inch photo, 400 X400 pixels/inch. 38.4MB.
• Voice PCM/ADPCM, 4kHz, 64kbps (this as well the
  followings called stream)
• Music/Audio
• MPEG/MP3, 16-24 kHz, 512-748 kbps.
• Video a sequence of pictures (moving pictures)
• H.261, 176 X 144 pixels/frame, 10-30
  frames/second, 2 Mbps.
• MPEG-2, 720 X 480 pixels/frame, 30 frames/second,
  249 Mbps.
• Compression
• 249Mbps ? 2 6 Mbps.
• Compression cost, but reduce the transmission
  cost.

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(Digital) Transmission System
Transmitter
Receiver
0110101
0110101
Communication channel
Figure 3.5
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Basic properties of digital transmission systems

• Bit rate or transmission speed R bits/second.
• Can be viewed as cross-section of the channel
  the higher R is, the larger the volume of the
  channel.
• Bandwidth of a signal Ws
• The range of frequencies contained in the signal.
  
• Bandwidth of channel Wc
• The range of input frequencies passed by the
  channel.
• Wc limits Ws that can pass through the channel.

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Basic properties of digital transmission systems
(cont.)

• Theory if WcW, then the narrowest pulse has
  duration ?1/2W. Thus, the maximum rate for
  pulses is rmax2W pulses/second.
• If transmitting binary information by sending two
  kinds of pulses A for 1 and _A for 0, then the
  system bite rate is R2W pulses/second
  1bit/pluse 2W bits/second.
• If pulses can be multiple levels (M4) -A, -A/3,
  A/3, A for (00, 01, 10,11), then each pulse can
  represent 2 bits. So R4W bps.
• If multiple levels M2m, then R2W m2Wm bps.
• Theoretically, the bit rate R can be increased
  without limits as long as we increase M.

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Shannon Channel Capacity

• Unfortunately, in practice, R is greatly limited
  
• Levels can not be measured accurately if too many
  levels.
• there exists noise in real world.
• Signal to-noise ratio SNR average signal
  power/average noise power.
• SNR(dB)10log10SNR (decibels).
• So Shannon Channel Capacity
• C (i.e., maximum reliable bite rate R )
• W log 2(1SNR) bits/second.

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Figure 3.11
18
When too many levels 1. difficult to measure
2. noise will
easily affect the value.
Figure 3.32
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Telephone Modem example

• W3.4 kHz, SNR10,000, SNR(dB)40 dB.
• C3400log2(110000) 45200 bits/second.
• So telephone channel is at 45.2kbps.
• Interesting point V.90 models rate 56kbps.
• Inbound to network 33.6kbps
• Analog to digital, quantization noise, SNR39 dB.
• Outbound to user from ISP already in digital.

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Bit Rates of Digital Transmission Systems
System Bit Rate Observations
Telephone twisted pair 33.6-56 kbps 4 kHz telephone channel
Ethernet twisted pair 10 Mbps, 100 Mbps 100 meters of unshielded twisted copper wire pair
Cable modem 500 kbps-4 Mbps Shared CATV return channel
ADSL twisted pair 64-640 kbps in, 1.536-6.144 Mbps out Coexists with analog telephone signal
2.4 GHz radio 2-11 Mbps IEEE 802.11 wireless LAN
28 GHz radio 1.5-45 Mbps 5 km multipoint radio
Optical fiber 2.5-10 Gbps 1 wavelength
Optical fiber gt1600 Gbps Many wavelengths
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Line Coding

• How to converting binary information sequence
  into digital signal.
• Consideration of choices (apart from bit rate)
• Average transmission power
• Ease of bit timing (synchronization)
• Prevention of dc and low-frequency content
• Ability of error-detection
• Immunity to noise and interference
• Cost and complexity.

22
Various line coding

• Unipolar nonreturn-to-zero encoding (NRZ)
• 1 A, 0 0 voltage.
• Polar NRZ
• 1 A/2, 0 -A/2
• Bipolar encoding
• 0 0 voltage, consecutive 1s are alternately
  mapped to A/2, -A/2.
• NRZ inverted (Differential encoding)
• 1 a transition at the beginning of a bit time.
• 0 no transition.
• Manchester encoding (used in Ethernet)
• 1 a transition from A/2 to A/2 in the middle
  of a bit time
• 0 a transition from -A/2 to A/2 in the middle
  of a bit time
• Differential Manchester encoding (used in
  Token-ring networks)
• A transition in middle of each bit time
• 1 absence of transition
• 0 a transition at the beginning of an interval.

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0
1
0
1
1
1
0
0
1
Unipolar NRZ
1 A, 0 0 voltage
Polar NRZ
1 A/2, 0 -A/2
NRZ-Inverted (Differential Encoding)
1 transition, 0 not
Bipolar Encoding
0 0 voltage, 1s are alternately mapped to A/2,
-A/2.
Manchester Encoding
1 a transition from A/2 to A/2, 0 otherwise
Differential Manchester Encoding
2 pulses/bit, 1 ?10, 0?01
A transition in middle of each bit time, 1
absence of transition,0 a transition at the
beginning.
Figure 3.35
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mBnB encoding (ngtm)

• Means m bits information are mapped to n encoded
  bits.
• Manchester encoding is 1B2B.
• Optical transmission 4B5B.
• FDDI 8B10B is used.

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Transmission Media

• Twisted Pair
• DSL, LAN (Ethernet), ISDN
• Coaxial Cable
• Cable TV, Cable Modem, Ethernet.
• Optical Fiber
• Backbone, LAN
• Radio Transmission
• Cellular network, Wireless LAN, Satellite
  network.
• Infrared Light
• IrDA Links

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Transmission Delay

• L number of bits in message
• R bps speed of digital transmission system
• L/R time to transmit the information
• tprop time for signal to propagate across
  medium
• d distance in meters
• c speed of light (3x108 m/s in vacuum)

Delay tprop L/R d/c L/R seconds

• Use data compression to reduce L
• Use higher speed modem to increase R
• Place server closer to reduce d

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Error Detection and Correction

• Error detection and retransmission
• When return channel is available
• Used in Internet
• Waste bandwidth
• Forward error correction (FEC)
• When the return channel is not available
• When retransmission incurs more cost
• Used in satellite and deep-space communication,
  as well as audio CD recoding.
• Require redundancy and processing time.

28
Odd error detection using parity bit

• Seven data bit plus 1 parity bit
• 1011010 0
• 1010001 1
• Then any odd errors can be detected.

29
Two-dimension parity checks
1 0 0 1 0 0 0 1 0 0 0 1 1 0 0 1 0 0 1 1 0 1 1
0 1 0 0 1 1 1

1. Several information rows
2. Last column check bits for rows
3. Last row check bits for columns

Can detect one, two, three errors, But not all
four errors.
1 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 0 0 1 1 0 1 1
0 1 0 0 1 1 1
1 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 0 0 1 0 0 1 1
0 1 0 0 1 1 1
1 0 0 1 0 0 0 0 0 1 0 1 1 0 0 1 0 0 1 0 0 1 1
0 1 0 0 1 1 1
1 0 0 1 0 0 0 0 0 1 0 1 1 0 0 1 0 0 1 0 0 0 1
0 1 0 0 1 1 1
2 errors
3 errors
4 errors
1 error
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Internet Checksum

• IP packet, a checksum is calculated for the
  headers and put in a field in the header.
• Goal is easy/efficient to implement, make routers
  simple and efficient.
• Suppose m 16-bit words, b0, b1, , bm-1
• Compute x b0 b1 bm-1 mod 216 -1
• Set checksum bm-x
• Insert x in the checksum field
• Verify b0 b1 bm-1 bm0 mod 216 -1.

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CRC (Cyclic Redundancy Check) (chapter 3.9.4)

• Based on polynomial codes and easily implemented
  using shift-register circuit
• Information bits, codewords, error vector are
  represented as polynomials with binary
  coefficients. On the contrary, the coefficients
  of a polynomial will be a binary string.
• Polynomial arithmetic is done modulo 2 with
  addition and subtraction being Exclusive-OR, so
  addition and subtraction is the same.
• Examples 10110 ??x4 x2 x
• 01011 ??x3 x 1

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Addition
11000001 01100000 10100001
Multiplication
00000011 00000111 00001001
1110
q(x) quotient
x3 x2 x
) 01100000
00001011
Division
x3 x 1 ) x6 x5
1011
x6 x4 x3
dividend
1110
divisor
1011
x5 x4 x3
1010
x5 x3 x2
1011
3
10
35 ) 122
x4 x2
105
x4 x2 x
17
x
r(x) remainder
polynomial arithmetic
Figure 3.55
33
How to compute CRC

• There is a generator polynomial, g(x) of degree
  r, which the sender and receiver agree upon in
  advance.
• Suppose the information transmitted has m bits,
  i.e. i(x), then sender appends r zero at the end
  of information, i.e, xr i(x)
• Perform xr i(x) / g(x) to get remainder r(x) (and
  quotient q(x))
• Append the r bit string of r(x) to the end of m
  bit information to get mr bit string, i.e.,
  b(x), for transmission.
• b(x) xr i(x) r(x) ( g(x)q(x)r(x)r(x)g(x)q(
  x) )
• When receiver receives the bit string, i.e.,
  b(x), it will divide b(x) by g(x) , if the
  remainder is not zero, then error occurs.
• --suppose no error occurs, then b(x) b(x), so
  b(x)/g(x)
• b(x)/g(x)g(x)q(x)/g(x)q(x), remainder is
  0.

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Example of CRC encoding

• Generator polynomial g(x) x3 x 1 ??1011
• Information (1,1,0,0) i(x) x3 x2
• Encoding x3i(x) x6 x5
  

x3 x2 x
1110
x3 x 1 x6 x5
1011 ) 1100000
x6 x4 x3
1011
x5 x4 x3
1110
1011
x5 x3 x2
1010
x4 x2
1011
x4 x2 x
x
010
Transmitted codeword b(x) x6 x5 x
b (1,1,0,0,0,1,0)
Figure 3.57
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Example of CRC encoding (cont.)
If 1100010 is received, then 1100010 is divided
by 1011, The remainder will be zero (please
verify yourself), so no error.
Suppose 1101010 is received, then let us do the
division as follows
1111
) 1101010
1011
1011
1100
1011
1111
1011
1000
1011
The remainder is not zero, so error occurs.
11
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Typical standard CRC polynomials

• CRC-8 x8 x2 x 1 ATM header
  error check
• CRC-16 x16x12x51 HDLC, XMODEM,
  V.41
• CRC-32 x32x26x23x22 IEEE 802, DoD,
  V.41,
• x16x12x11x10 AAL5
• x8x7x5x4x2x1

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Analysis of error detection power
Received poly R(x) b(x) e(x), where e(x) is
error poly.

• 1. Single errors e(x) xi 0 ? i ? n-1
• If g(x) has more than one term, it cannot divide
  e(x)
• 2. Double errors e(x) xi xj 0 ? i lt
  j ? n-1
• xi (1 xj-i )
• If g(x) is primitive, it will not divide (1
  xj-i ) for j-i ? 2n-k?1
• 3. Odd number of errors e(1) 1.
• If g(x) has (x1) as a factor, then g(1) 0 and
  all codewords have an even number of 1s.

Figure 3.60
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The error detection capabilities of CRCs

• As long as the g(x) is selected appropriately
• All single errors
• All double errors
• All odd number of errors
• Burst error of length L, the probability that
  this burst error is undetectable 1/2(L-2)
• CRC can be easily implemented in hardware
• One word about error correction more powerful,
  but need more extra check bits, more slow, so not
  use as much as error detection.

39
Statistical multiplexing

• Burst feature of user interactions makes
  dedicated communication lines inefficient
• Multiplexing multiple lines into one line which
  has generally more bandwidth.
• In order for coordinating the usage of the shared
  line, buffers are needed.
• Multiplexers are introduced for multiplexing

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Input lines
A
Output line
B
Buffer
C
Figure 5.42
41
(a)
A
A
B
B
C
C
Figure 4.1
42
Time-Division Multiplexing (TDM)
(a)
A1
Dedicated Lines
A2
B1
B2
C2
C1
(b)
Shared Line
B2
C2
A2
B1
C1
A1
Figure 5.43
43
1
1
2
MUX
MUX
2
. . .
. . .
22
24
b
1
2
23
24
. . .
b
24
frame
24
T-1 carrier system uses TDM to carry 24 digital
signals in telephone system
Figure 4.4
44
Wavelength-division multiplexing (WDM)
?1, ?2, ?n
MUX
deMUX
Optical fiber
Figure 4.1
45
Frequency-Division Multiplexing (FDM)
(a) Individual signals occupy W Hz
(b) Combined signal fits into channel bandwidth
Figure 4.2