Digital transmission fundamentals (chap.3 & 4)

1. What is digital transmission?

2. Why digital transmission?

3. How to represent different information in digital format? 4. What is Bit rate/bandwidth?

5. What are the properties of different media?

6. How to do error detection and correction?

7. Multiplexing?

CIS, IUPUI 1

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.

CIS, IUPUI 2

CIS, IUPUI

(a) . . .

1 0 1 0 1 0 1 0 . . .

t

(b) . . .

1 ms 1 1 1 1 0 0 0 0 . . .

t

1 ms CIS, IUPUI

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: W=4 kHz,

sampling rate

=8K samples/second. Sample period is T=1/8000=125 microseconds. Suppose 8 bits/sample (256 levels), then kbps.

PCM bit rate

is 8000*8=64 CIS, IUPUI 5

(a) 7D/2 5D/2 3D/2 D/2 -D/2 -3D/2 -5D/2 -7D/2 (b) 7D/2 5D/2 3D/2 D/2 -D/2 -3D/2 -5D/2 -7D/2 CIS, IUPUI 6 Figure 3.2

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.

CIS, IUPUI 7

(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 Sent Received • e.g digital telephone, CD Audio CIS, IUPUI 8 Figure 3.6

Transmission segment Source Repeater Repeater Destination CIS, IUPUI 9 Figure 3.7

Attenuated & distorted signal + noise Amp.

Equalizer Repeater Recovered signal + residual noise CIS, IUPUI 10 Figure 3.8

Amplifier Equalizer Timing Recovery Decision Circuit.

& Signal Regenerator Distorted Digital signal is easy to restore by regenerator. CIS, IUPUI 11 Figure 3.9

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.

CIS, IUPUI 12

Transmitter Transmitter 0110101… (Digital) Transmission System Communication channel Receiver Communication channel Receiver 0110101… CIS, IUPUI 13 Figure 3.5

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.

CIS, IUPUI 14

Basic properties of digital transmission systems (cont.) • Theory: if Wc=

W

, then the narrowest pulse has duration  =1/2

W

. Thus, the maximum rate for pulses is

r max

=2

W

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

R

=2

W

pulses/second * 1bit/pluse =2

W

bits/second.

• If pulses can be multiple levels ( R=4

W

bps.

• If multiple levels

M

=2

m

, then

R M

=2 =4): -A, -A/3, +A/3, +A for (00, 01, 10,11), then each pulse can represent 2 bits. So

W

*

m

=2

Wm

bps.

• Theoretically, the bit rate as long as we increase

M

.

R

can be increased without limits CIS, IUPUI 15

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)=10log 10 SNR (decibels).

• So Shannon Channel Capacity: – –

C

(i.e., maximum reliable bite rate

R

) =

W

log 2 (1+SNR) bits/second. CIS, IUPUI 16

High SNR Low SNR Signal Noise Signal + noise

t

Signal Noise

t

SNR = Average signal power Average noise power SNR (dB) = 10 log 10 SNR CIS, IUPUI

t t

Signal + noise

t t

Typical noise Four signal levels Eight signal levels When too many levels: 1. difficult to measure 2. noise will easily affect the value.

CIS, IUPUI

Telephone Modem example

• W=3.4 kHz, SNR=10,000, SNR(dB)=40 dB.

• C=3400log 2 (1+10000) =45200 bits/second.

• So telephone channel is at 45.2kbps. • Interesting point: V.90 model’s rate: 56kbps.

– Inbound to network: 33.6kbps • Analog to digital, quantization noise, SNR=39 dB.

– Outbound to user from ISP: already in digital.

CIS, IUPUI 19

Bit Rates of Digital Transmission Systems

System Telephone twisted pair Bit Rate 33.6-56 kbps Ethernet twisted pair 10 Mbps, 100 Mbps Cable modem 500 kbps-4 Mbps Observations 4 kHz telephone channel 100 meters of unshielded twisted copper wire pair Shared CATV return channel ADSL twisted pair 64-640 kbps in, 1.536 6.144 Mbps out 2.4 GHz radio 2-11 Mbps 28 GHz radio 1.5-45 Mbps Optical fiber Optical fiber 2.5-10 Gbps >1600 Gbps Coexists with analog telephone signal IEEE 802.11 wireless LAN 5 km multipoint radio 1 wavelength CIS, IUPUI Many wavelengths 20

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.

CIS, IUPUI 21

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. CIS, IUPUI 22

Unipolar NRZ

1: +A, 0: 0 voltage

1 Polar NRZ

1: +A/2, 0: -A/2

0 1 0 1 1 1 0 0 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 2 pulses/bit, 1  10, 0  01 Manchester Encoding 23

A transition in middle of each bit time, 1: absence of transition,0: a transition at the beginning.

Figure 3.35

m

B

n

B encoding (

n

>

m

)

• Means “

m

bits information are mapped to

n

encoded bits.

• Manchester encoding is 1B2B.

• Optical transmission 4B5B.

• FDDI: 8B10B is used.

CIS, IUPUI 24

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 CIS, IUPUI 25

• • • • • •

L R

bps

L/R t

prop

d c

Transmission Delay

number of bits in message speed of digital transmission system time to transmit the information time for signal to propagate across medium distance in meters speed of light (3x10 8 m/s in vacuum)

Delay = t prop + 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 CIS, IUPUI 26

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.

CIS, IUPUI 27

Odd error detection using parity bit

• Seven data bit plus

1 parity bit

• 1011010

0

• 1010001

1

• Then any odd errors can be detected.

CIS, IUPUI 28

Two-dimension parity checks

1.

2.

3.

Several information rows Last column: check bits for rows Last row: check bits for columns Can detect one, two, three errors, But not all four errors.

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 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 1 error 2 errors CIS, IUPUI 3 errors 4 errors 29

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, b 0 , b 1 , …, b

m

-1 – Compute x= b 0 + b 1 + …+ b

m

-1 – Set checksum b

m

=-x mod 2 16 -1 – Insert x in the checksum field – Verify b 0 + b 1 + …+ b

m

-1 + b

m

=0 mod 2 16 -1.

CIS, IUPUI 30

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 

x 4

01011 

x 3 + x 2 + x + x + 1

CIS, IUPUI 31

Addition: Multiplication: (

x

7 

x

6  1)  (

x

6 

x

5 ) 

x

7  (1  1)

x

6 

x

5  1 

x

7 

x

5  1 11000001 + 01100000 = 10100001 (

x

 1)(

x

2 

x

 1) 

x

3 

x

2 

x



x

2 

x

 1 

x

3  1 00000011 * 00000111 = 00001001 Division: divisor 3 35 ) 122 105 17

x

3 +

x

+ 1 )

x x x

3 6 6 + + +

x x

5

x

2 5

x

+

x

5 +

x

4 +

x

3 +

x

4 4

x

+

x x

3 3 + +

x x

=

q(x)

quotient 00001011 2 2

x

4 +

x

2 +

x

dividend 1110 ) 01100000 1011 1110 1011 1010 1011 10

x

=

r(x)

remainder

polynomial arithmetic

CIS, IUPUI 32 Figure 3.55

How to compute CRC

• There is a generator polynomial, g

(x)

of degree sender and receiver agree upon in advance.

r,

which the • Suppose the information transmitted has

m

bits, i.e.

i(x)

, then sender appends

r

zero at the end of information, i.e,

x r i(x)

• Perform

x r i(x)

• Append the

r

/ g

(x)

to get remainder bit string of

r(x) r(x)

to the end of (and quotient

q(x)

)

m

bit information to get

m+r

bit string, i.e.,

b(x),

for transmission.

–

b(x) = x r 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

.

CIS, IUPUI 33

Example of CRC encoding

Generator polynomial: g

(x)= x 3 + x +

1  1011 Information: (1,1,0,0)

i(x) = x 3 + x 2

Encoding:

x 3 i(x) = x 6 x 3 + x 2 + x + x 5

1110

x 3 + x +

1

x 6 + x 5 x 6 + x 4 + x 3

1011 ) 1100000 1011

x 5 + x 4 + x 3 x 5 + x 3 + x 2

1110 1011

x 4 + x 2 x 4 + x 2 + x

1010 1011

x

Transmitted codeword:

b(x) = x 6 + x 5 + x

010

b

= (1,1,0,0, 0,1,0 ) CIS, IUPUI 34 Figure 3.57

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: 1011 1111 ) 1101010 1011 1100 1011 1111 1011 1000 1011 11 CIS, IUPUI

The remainder is not zero, so error occurs.

35

Typical standard CRC polynomials

• CRC-8:

x 8 + x 2 + x + 1

ATM header error check • CRC-16:

x 16 +x 12 +x 5 +1

HDLC, XMODEM, V.41

• CRC-32:

x 32 +x 26 +x 23 +x 22 +

IEEE 802, DoD, V.41,

x 16 +x 12 +x 11 +x 10 + x 8 +x 7 +x 5 +x 4 +x 2 +x+1

AAL5 CIS, IUPUI 36

Analysis of error detection power Received poly: R(

x

)=

b

(

x

) +

e

(

x

), where

e

(

x

) is error poly.

1. Single errors: e(x) = x

i

0 

i



n

-1 If

g(x)

has more than one term, it cannot divide

e(x)

2. Double errors:

e(x)

=

x i

+

x j

0 

i

<

j



n

-1 If

g(x)

=

x i

(1 +

x j-i

) is primitive, it will not divide (1 +

x j-i

) for

j-i

 2

n-k

1

3. Odd number of errors:

e

(1) =1.

If

g(x)

has (

x

+1) as a factor, then

g

(1) = 0 and all codewords have an even number of 1s.

CIS, IUPUI 37 Figure 3.60

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.

CIS, IUPUI 38

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 CIS, IUPUI 39

A B C Input lines Header Buffer Data payload Output line CIS, IUPUI 40 Figure 5.42

(a) A B C A B C (b) A B C MUX

Trunk group

MUX A B C CIS, IUPUI 41 Figure 4.1

Time-Division Multiplexing (TDM) (a) Dedicated Lines (b) Shared Line

A 1 B 1 C 1 A 1 C 1 B 1 A 2 B 2 C 2 A 2 B 2 C 2

CIS, IUPUI 42 Figure 5.43

1 2 MUX 24 22 23 24 b 1 2

frame . . .

24 b MUX 1 2 24 T-1 carrier system uses TDM to carry 24 digital signals in telephone system CIS, IUPUI 43 Figure 4.4

Wavelength-division multiplexing (WDM)  1  2 

n

MUX  1 ,  2 , 

n

Optical fiber deMUX  1  2 

n

CIS, IUPUI 44 Figure 4.1

Frequency-Division Multiplexing (FDM)

(a) Individual signals occupy

W

Hz 0 A

W f

0 B

W

C 0

W f f

(b) Combined signal fits into channel bandwidth A B C

f

CIS, IUPUI 45 Figure 4.2