lec6 line codes

8/10/2019 Lec6 Line Codes

http://slidepdf.com/reader/full/lec6-line-codes 1/22

TE312: Introduction to

Digital Telecommunications

PART IIBASEBAND DIGITAL

TRANSMISSION

Lecture #6

PCM Waveforms



IntroductionPoints to be discussed in this lecture

• PCM Waveforms (Line Codes)

• Types of Line Codes

•Characteristics of Line Codes



Introduction

Reading Assignment

Simon Haykin, “Digital Communications”,John Wiley & Sons, Inc., 1988, Chapter 5,Sec. 5.1, Sec. 5.3 and Sec. 5.4.

Bernard Sklar, “Digital Communications:Fundamentals and Applications,” 2 nd Ed.,Prentice Hall, 2000, Chapter 2, Sec. 2.8.



Line Codes

A pulse code modulation (PCM) systemconverts an analog message signal into a

sequence of binary digits (bits).

For transmission of binary data through a

baseband channel, each bit in the bitstream is represented with an electricalpulse.

The resulting baseband binary waveformis called a PCM waveform or line code.



Line Codes The following block diagram models a linecoder.

( )s t na Line

Coder

The input is a sequence of values whichis a function of the thn data bit

na

[ ]0, 1nb ∈ .

The output ( )s t is a waveform, expressedas



Line Codes

( ) ( )n bn

s t a g t nT ∞

=−∞

= −∑

( )where g t is a pulse shape and is the bitperiod.

bT

For a PCM system, n/b sT T = with samplingperiod sT and number of bits per sample .n

Three basic mapping na are unipolar ,polar (antipodal) and bipolar(pseudoternary).

nb ⇒



Line Codes (i) Unipolar Mapping

( ), for 1 (mark)

0, for 0 spacen

nn

A ba

b

=⎧= ⎨ =⎩

(ii) Polar (Antipodal) Mapping

( ), for 1 (mark)

, for 0 spacen

nn

A ba

A b

+ =⎧= ⎨− =⎩



Line Codes (iii) Bipolar (Pseudoternary) Mapping

( )( )

1

1

, for 1 (mark) and

, for 1 mark and

0, for 0 space

n n

n n n

n

A b a A

a A b a A

b

−

−

⎧+ = = −⎪

= − = =⎨

⎪ =⎩

Three basic pulse shapes ( )g t are non-return-to-zero (NRZ) , return-to-zero (RZ) and split-phase are defined as follows.



Line Codes

Pulse shapes are defined assuming thateach bit is centered on an integer multiple

of .bT

(i) Non-Return-to-Zero (NZR) pulseshape

( )1, /2

0, elsewhereb

b

t T t g t T

⎧ ≤⎛ ⎞

= Π = ⎨⎜ ⎟⎝ ⎠ ⎩

1

/ 2bT − / 2bT t

( )g t



Line Codes

(ii) Return-to-Zero (RZ) pulse shape

( ) 1, /4/ 2 0, elsewhere

b

b

t T t g t T

⎧ ≤⎛ ⎞= Π = ⎨⎜ ⎟⎝ ⎠ ⎩

1

/ 4bT − / 4bT

( )g t

t



Line Codes

(iii) Split-Phase pulse shape

( )1, - / 2 0

/ 4 / 4 1, 0 / 2/ 2 / 2bb b

bb b

T t t T t T g t t T T T

+ ≤ ≤⎛ ⎞ ⎛ ⎞ ⎧+ −= Π − Π = ⎨⎜ ⎟ ⎜ ⎟ − ≤ ≤⎩⎝ ⎠ ⎝ ⎠

t / 2bT

/ 2bT −

1

1−

( )g t



Types of Line Codes

(ii) Unipolar RZ Line Code: This codeuses the unipolar mapping and theRZ pulse shape.

1 0 1 0 0 1 1nb

na A 0 A0 0

( )s t

t



Types of Line Codes (iii) Polar NRZ Line Code: This code uses

the polar (antipodal) mapping and theNRZ pulse shape.

A A−− A A− A

100101 nb 1

na

( )s t



Types of Line Codes

(iv) Polar RZ Line Code: This code usesthe polar (antipodal) mapping and the

RZ pulse shape.

nb 1 0 1 0 0 1 1

na A − A− A− A

( )t

t

s



Types of Line Codes

(v) Bipolar NRZ Line Code: This codeuses the bipolar (pseudoternary)

mapping and the NRZ pulse shape.

nb

1 00 1 0 1 1

na A 0 A− −0 0

( )s t

t



Types of Line Codes

(vi) Bipolar RZ Line Code: This codeuses the bipolar (pseudoternary,

alternate mark inversion - AMI)mapping and the RZ pulse shape.

nb 1 00 1 0 1 1

na 0 A − 0 0 A A−

( )t

t

s



Types of Line Codes

(vii) Manchester Line Code: This codeuses the polar (antipodal) mapping

and the split-phase pulse shape.

t

A− −

1 0 1 0 0 1 1nb

A A− A A na

( )s t



Characteristics of Line CodesDesirable Properties of Line codes

(i) Self-Synchronization Several line codes provideinformation for recovering timing ofthe start and the end of each bit.

Manchester codes have the best self-synchronization capability as theyalways have a zero crossing in thecenter of each bit.



Characteristics of Line Codes

Polar RZ codes have good self-synchronization capability.

NRZ codes have poor self-synchronization capability.

(ii) Noise Immunity

Some line codes perform better thanthe others in combating channelnoise and interference with lowprobability of bit error.




Polar line codes perform better thanunipolar or bipolar codes i.e. for the

same energy per bit, polar line codesexhibit less probability of bit error.

(iii) Error Detection

Some line codes provide the receiverwith the ability to detect bit errorsdue to channel noise.




(iv) Signal Power Spectral Density

Line codes are desired to occupysmall bandwidth. In some cases, it isdesired for the line codes to have no

dc components, which allows for ACcoupling using transformers.

(v) Cost and Complexity ofImplementation

lec6 line codes

Documents