Sami Al-Wakeel 1 Data Transmission and Computer Networks Data Encoding.

Sami Al-Wakeel1

Data Transmission and Computer Networks

Data Encoding

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Data Encoding

Analog and digital data can be encoded into either digital or analog signal, creating four possible combinations:

1- Digital Data, Digital Signal.

2- Analog Data, Digital Signal.

3- Digital Data, Analog Signal.

4- Analog Data, Analog Signal.

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Data Encoding

1. Digital Data, Digital Signals: Binary data are transmitted by encoding

each data bit into signal element. Factors determine how successful the

receiver will interpret the incoming signal:– An increase in data rate increases bit error

rate.– An increase in S/N decreases bit error rate.– An increase in bandwidth allows an increase in

data rate.

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Data Encoding

1. Digital Data, Digital Signals (Continued):

Polar

NRZ RZ Biphase

NRZ-L Manchester Differential

Manchester

NRZI

Bipolar

AMI B8ZS HDB3

Digital Signal Encoding

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Data Encoding

1. Digital Data, Digital Signals (Continued):

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Data Encoding

1. Digital Data, Digital Signals (Continued):

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Data Encoding

1. Digital Data, Digital Signals (Continued):

Digital signal Encoding Formats:

I. NonReturn-to-Zero-Level (NRZ-L) Encoding: A negative voltage is equated with binary 1 and a positive voltage

with binary 0.

II. NonReturn to Zero Inverted (NRZI) Encoding: Binary 0 is represented by no transition at the beginning of bit

interval, and binary 1 is represented by a transition at beginning of bit interval.

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Data Encoding

1. Digital Data, Digital Signals (Continued):

Advantages of NRZ:– The NRZ codes are simple and make efficient use of

bandwidth.

Disadvantages of NRZ: – Lack of synchronization capability. Consider a long

string of 1’s or 0’s for NRZ-L, or a long string of 0’s for NRZI, the output is a constant voltage over a long period of time.

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Data Encoding

1. Digital Data, Digital Signals (Continued):

III. Bipolar-AMI Encoding: A binary 0 is represented by no line signal, and a binary 1

is represented by a positive or negative pulse. The binary 1 pulse must alternate in polarity.

IV. Pseudoternary Encoding: A binary 1 is represented by no line signal, and a binary 0

by alternating positive or negative pulses.

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Data Encoding

1. Digital Data, Digital Signals (Continued): Advantages of Bipolar-AMI or Pseudoternary:

– No loss of synchronization if long string of binary 1’s occurs in the case of AMI or 0’s in the case of Pseudoternary.

– The pulse alternation property provides a simple means of error detection.

Disadvantages of Bipolar-AMI or Pseudoternary:– Long string of binary 0’s in the case of AMI or 1’s in

the case of Pseudoternary still present a problem.– Multilevel binary signal requires approximately 3 dB

more signal power than a two-valued signal for the same probability of bit error.

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Data Encoding

1. Digital Data, Digital Signals (Continued):

V. Manchester Encoding: There is a transition at the middle of each bit period. The mid-bit transition serves as a clocking mechanism

and also as data. A low-to high transition represents a binary 1, and a

high-to-low transition represents a binary 0.

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Data Encoding

1. Digital Data, Digital Signals (Continued):

VI. Differential Manchester Encoding: There is a transition at the middle of each bit period. The mid-bit transition is used only to provide clocking. A binary 0 is represented by the presence of a transition at

the beginning of a bit period, and a binary 1 is represented by the absence of a transition at the beginning of a bit period

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Data Encoding

1. Digital Data, Digital Signals (Continued):Advantages of Manchester and Differential Manchester Encoding:

– Synchronization: Because this is a transition at the middle of each bit period.

– Error Detection: The absence of the expected transition can be used to detect errors.

Disadvantages of Manchester and Differential Manchester Encoding:

– High Signaling Rate: At least one transition per bit time is needed, and may have at maximum two transitions. Therefore, the maximum modulation rate (rate at which signal level is changed) is twice that for NRZ; this means the required bandwidth is greater.

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Data Encoding

Modulation Rate: Modulation rate is the rate at which signal elements are generated.

Minimum 101010 …

Maximum

NRZ-L0 (all 0’s or 1’s)

1.0 1.0

NRZI 0 (all 0’s) 0.5 1.0 (al1’s)

Bipolar-AMI 0 (all 0’s) 1.0 1.0

Pseudoternary 0 (all 1’s) 1.0 1.0

Manchester1.0 (101010 …)

1.0 2.0 (all 0’s or 1’s)

Differential Manchester

1.0 (all 1’s) 1.5 2.0 (all 0’s)

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Data Encoding

1. Digital Data, Digital Signals (Continued): VII. Bipolar with 8-zeros substitution (B8ZS): The coding scheme is based on a bipolar-AMI. The

encoding is updated with the following rules: – If an octet of all zeros occurs and the last voltage

pulse preceding this octet was positive, then the eight zeros of the octet are encoded as 0 0 0 + - 0 - + .

– If an octet of all zeros occurs and the last voltage pulse preceding this octet was negative, then the eight zeros of the octet are encoded as 0 0 0 - + 0+ - .

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Data Encoding

1. Digital Data, Digital Signals (Continued):

VII. Bipolar with 8-zeros substitution (B8ZS):

+

Polarity of previous bit

0 0 0 0 0 0 0 0

0 0 0 + - 0 - ++

Violation Violation

-

Polarity of previous bit

0 0 0 0 0 0 0 0

0 0 0 - + 0 + --

Violation Violation

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Data Encoding

1. Digital Data, Digital Signals (Continued):

VIII. High-density Bipolar-3 zeros (HDB3): HDB3 is based on the AMI encoding. HDB3 replaces strings of 4 zeros with sequences

containing one or two pulses. In each case, the fourth zero is replaced with a code

violation. In addition, successive violations are of alternate

polarity. Thus, if the last violation was positive, this violation must be negative, and vice versa.

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Data Encoding

1. Digital Data, Digital Signals (Continued):

VIII. HDB3(Continued): The following table shows the HDB3 substitution rules:

Polarity of Preceding

Pulse

Number of Bipolar Pulses (Ones) Since Last

Substitution

Odd Even

- 0 0 0 - + 0 0 +

+ 0 0 0 + - 0 0 -

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Data Encoding

1. Digital Data, Digital Signals (Continued):

VIII. HDB3(Continued):

0 0 0 0

0 0 0 +

0 0 0 0

0 0 0 --

-

+

+

0 0 0 0

- 0 0 -

0 0 0 0

+ 0 0 +-

-

+

+

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Data Encoding

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Data Encoding

2. Digital Data, Analog Signals: The most familiar of use of this transformation is for

transmitting digital data through the public telephone network.

The telephone network is designed to transmit, switch, and receive analog signals in the voice-frequency range of about 300 to 3400 Hz.

A telephone line will not pass low-frequency signals that could occur if the data stream is made up of a continuous string of binary 1s or 0s.

Thus digital devices are attached to the network via a modem (Modulator-demodulator) which coverts digital data to analog signals, and vice versa.

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Data Encoding

2. Digital Data, Analog Signals (Continued):

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Definitions

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Data Encoding

2. Digital Data, Analog Signals (Continued):

Encoding Techniques: There are three basic encoding or modulation

techniques for transforming digital data into analog signals:

– Amplitude-Shift Keying (ASK).– Frequency-Shift Keying (FSK).– Phase-Shift Keying (PSK).

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Data Encoding

2. Digital Data,

Analog Signals:

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Data Encoding

2. Digital Data, Analog Signals:

Bit rate is the number of bits per second. Baud rate is the number of signal elements per second. The baud rate equals the bit rate divided by the number

of bits represented by each signal element. The carrier signal is a high-frequency signal that acts as

a basis for information signal. The receiving device is turned to the frequency of the carrier signal that it expects from the sender.

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Data Encoding

2. Digital Data, Analog Signals (Continued):

Encoding Techniques:

ASK FSK PSK

QAM

Digital/analog Encoding

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Data Encoding

2. Digital Data,

Analog Signals:

I. Amplitude-Shift Keying:

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Data Encoding

2. Digital Data, Analog Signals (Continued):

I. Amplitude-Shift Keying (ASK): We can represent a unipolar periodic signal, vd(t), with unity

amplitude and fundamental frequency w0 as:

We can represent the carrier signal as:

ASK can be represented mathematically as:

...}5cos5

13cos

3

1{cos2

2

1)( 000 twtwtwtvd

twtv cc cos)(

)().()( tvtvtv dcASK

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Data Encoding

2. Digital Data, Analog Signals (Continued):

I. Amplitude-Shift Keying (ASK): However:

...}5cos.cos5

13cos.cos

3

1cos.{cos

2cos2

1)( 000 twtwtwtwtwtwtwtv ccccASK

twwtwwtwtv cccASK )cos(){cos(1

cos2

1)( 00

...})5cos(5

1)5cos(

5

1

)3cos(3

1)3cos(

3

1

00

00

twwtww

twwtww

cc

cc

)cos()cos(cos.cos2 BABABA

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Data Encoding

2. Digital Data,

Analog Signals:

II. Frequency-Shift Keying:

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Data Encoding

2. Digital Data, Analog Signals (Continued):II. Frequency-Shift Keying (FSK):FSK can be represented mathematically as:

w1 and w2 are the two carrier frequencies in radians per second.

twtv

twtv

where

tvtvtvtvtv

c

c

dcdcFSK

22

11

21

cos)(

cos)(

)](1).[()().()(

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Data Encoding

2.Digital Data, Analog Signals (Continued):II. Frequency-Shift Keying (FSK): An example of use of FSK for full-duplex operation

over the PSTN. The PSTN will pass frequencies in the approximate

range 300 to 3400 Hz. To achieve full-duplex, the bandwidth is split at 1700

Hz. In one direction, the frequencies used to represent 1

and 0 are centered on 1170 Hz. Similarly, for the opposite direction, the frequencies used to represent 1 and 0 are centered on 2125 Hz

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Data Encoding

2. Digital Data, Analog Signals:

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Data Encoding

2. Digital Data,

Analog Signals:

III. Phase-Shift Keying:

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Definitions

Relationship between different phases:

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Data Encoding

2. Digital Data, Analog Signals (Continued):

Multilevel Modulation Methods: More efficient use of bandwidth can be achieved

if each signaling element represents more than one bit. For example, instead of a phase shift of 180, Quadrature Phase-Shift Keying (QPSK) or (4-PSK) technique uses phase shifts of multiple of 90.

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Data Encoding

2. Digital Data, Analog Signals (Continued):

4-PSK:

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Data Encoding

8-PSK:

Tribit Phase

000 0

001 45

010 90

011 135

100 180

101 225

110 270

111 315

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Data Encoding

2. Digital Data, Analog Signals (Continued):

Quadrature Amplitude Modulation (QAM).Higher bit rates are achieved using 8 and even 16 phase

changes. In practice, however, there is a limit to how many phases can be used.

Hence to increase the bit rate further, it is more common to introduce amplitude as well as phase variations of each vector. This type of modulation is then known as Quadrature Amplitude Modulation (QAM).

16-QAM has 16 levels per signal element, and hence 4-bit symbols.

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Data Encoding

2. Digital Data, Analog Signals (Continued):

4-QAM (1 amplitude, 4 phases):

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Data Encoding

2. Digital Data, Analog Signals (Continued):

8-QAM (2 amplitudes, 4 phases):

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Data Encoding

2. Digital Data, Analog Signals (Continued):

16-QAM ( 4 amplitudes, 8 phases):

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Data Encoding

2. Digital Data, Analog Signals (MODEMS): A modem converts the digital signal generated by the

computer into an analog signal to be carried by a public phone line. It is also converts the analog signals receiver over a phone line into digital signals usable by the computer.

The term modem is composite word that refers to a signal modulator and a signal demodulator.

A modulator treats a digital signal as a series of 1s and 0s, and so can transform it into an analog signal by using the digital-to-analog mechanisms of ASK, FSK, PSK, and QAM.

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Data Encoding

2. Digital Data, Analog Signals (MODEMS):

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Data Encoding

2. Digital Data, Analog Signals (MODEMS):

Telephone Line Bandwidth:

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Data Encoding

Modem Speeds: Theoretical Bit Rates for Modems:

Encoding Half-Duplex Full-Duplex

ASK , FSK , 2-PSK 2400 1200

4-PSK , 4 QAM 4800 2400

8-PSK , 8-QAM 7200 3600

16-QAM 9600 4800

32-QAM 12000 6000

64-QAM 14400 7200

128-QAM 16800 8400

256-QAM 19200 9600

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Data Encoding

3. Analog Data, Digital Signals:

A process of converting analog data into digital data, which process is known as digitization.

The device used for converting analog data into digital form for transmission, and subsequently recovering the original data from the digital is known as a codec (coder-decoder)

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Data Encoding

3. Analog Data, Digital Signals (Continued):

Voice transmissions are limited to a maximum bandwidth of less than 4 KHz.

To Convert such signals into digital form, the Nyquest sampling theorem states:

If a signal f(t) is sampled at regular intervals of time and at the rate higher than twice the highest frequency component, then the samples contain all the information of the original signal. The function f(t) may be reconstructed from these samples.

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Data Encoding

3. Analog Data, Digital Signals (Continued):

Hence to convert a 4 KHz voice signal into digital form, it must be sampled at rate of 8000 times per second.

The sampled signal is first converted into a pulse stream, the amplitude of each pulse being equal to the amplitude of the original analog signal at the sampling instant. The resulting signal is known as a pulse amplitude modulated (PAM) signal.

The PAM signal is still analog since its amplitude can vary over the full amplitude range.

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Data Encoding

3. Analog Data, Digital Signals (Continued):

It is converted into an all-digital form by quantizing each pulse into its equivalent binary form.

If eight bits are used to quantize each PAM signal, then 256 distinct levels are used.

The resulting digital signal is known as a pulse code modulated (PCM) signal and has a bit rate of 64 kbps – 8000 sample per second each of 8 bits.

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Data Encoding

3. Analog Data,

Digital Signals:

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Data Encoding

3. Analog Data, Digital Signals: