1. Line Codes and Their Spectra
Chapter 3:
Line Codes and Their Spectra
Types of Line Codes
Comparison of Line Codes
PSD of Line Codes
Huseyin Bilgekul
Eeng360 Communication Systems I
Department of Electrical and Electronic Engineering
Eastern Mediterranean University

2. Line Codes in PCM
The output of an ADC can be transmitted over a baseband channel.
The digital information must first be converted into a physical signal.
The physical signal is called a line code. Line coders use the terminology mark to mean binary one and space to mean binary zero.
ADC
PCM signal
Sample
Quantize
Analog
Input
Signal
Encode
Line
Code X XQ Xk
x(t)

3. Line codes (a) Punched Tape (b) Unipolar NRZ (c) Polar NRZ
BINARY DATA
(a) Punched Tape
Mark (hole)
Mark (hole)
space
Mark (hole)
space
space
Mark (hole)
Volts A
(b) Unipolar NRZ Tb
Time A
(c) Polar NRZ -A A
(d) Unipolar RZ A
(e) Bipolar RZ -A A
(f) Manchester NRZ -A
Binary Signaling Formats

4. Goals of Line Coding A line code is designed to meet several goals:
Self-synchronization.
The ability to recover timing from the signal itself.
Long series of ones and zeros could cause a problem.
Low probability of bit error.
The receiver needs to be able to distinguish the waveform associated with a mark from the waveform associated with a space, even if there is a considerable amount of noise and distortion in the channel.
Spectrum that is suitable for the channel.
In some cases DC components should be avoided if the channel has a DC blocking capacitance.
The transmission bandwidth should be minimized.

5. Line Coder
Line Coder
Digital
Data
Physical
Waveform
The input to the line encoder is a sequence of values ak that is a function of a data bit or an ADC output bit.
The output of the line encoder is a waveform:
Where p(t) is the Pulse Shape and Tb is the Bit Period
Tb =Ts/n for n bit quantizer (and no parity bits).
Rb =1/Tb=nfs for n bit quantizer (and no parity bits).
The operational details of this function are set by the particular type of line code that is being used.

6. Types of Line Codes
Each line code is described by a symbol mapping function ak and a pulse shape p(t):
Categories of line codes:
Symbol mapping functions (ak).
Unipolar
Polar
Bipolar (a.k.a. alternate mark inversion, pseudoternary)
Pulse shapes p(t).
NRZ (Nonreturn-to-zero)
RZ (Return to Zero)
Manchester (split phase)

7. Unipolar NRZ Line Code
The unipolar nonreturn-to-zero line code is defined by the unipolar mapping:
where Xk is the kth data bit.
In addition, the pulse shape for unipolar NRZ is:
Where Tb is the bit period.
Hard to recover symbol timing
when long string of 0s or 1s.
Note the DC component
This means wasted power! 1 1 1 1

8. Unipolar RZ Line Code
The unipolar return-to-zero line code has the same symbol mapping but a different pulse shape than unipolar NRZ:
Long strings of 1’s no longer a problem.
However strings of 0’s still problem.
Pulse of half the duration of NRZ
requires twice the bandwidth! 1 1 1 1

9. Polar Line Codes Polar line codes use the antipodal mapping:
Polar NRZ uses NRZ pulse shape.
Polar RZ uses RZ pulse shape.
No DC component,
so more energy efficient. 1 1 1 1
Polar NRZ
Now we can handle
long strings of 0’s, too.
Polar RZ

10. Manchester Line Codes
Manchester line codes use the antipodal mapping and the following split-phase pulse shape: 1
Easy synchronization and better spectral characteristics than polar RZ.

11. Bipolar Line Codes
With bipolar line codes a space is mapped to zero and a mark is alternately mapped to -A and +A:
Also called pseudoternary signalling and alternate mark inversion (AMI).
Either RZ or NRZ pulse shape can be used.
Bipolar (RZ) 1

12. Comparison of Line Codes
Self-synchronization:
Manchester codes have built in timing information because they always have a zero crossing in the center of the pulse.
Polar RZ codes tend to be good because the signal level always goes to zero for the second half of the pulse.
NRZ signals are not good for self-synchronization.
Error probability:
Polar codes perform better (are more energy efficient) than Unipolar or Bipolar codes.
Channel characteristics:
We need to find the PSD of the line codes to answer this ...

13. Power Spectra for Binary Line Codes
PSD can be calculated using the autocorrelation function:
A digital signal is represented by
f(t) - Symbol Pulse shape; Ts - Duration of one symbol;
Binary signaling : Ts= Tb , Multilevel signaling: Ts= lTb
PSD depends on:
(1) The pulse shape used
(2) Statistical properties of data expressed by the autocorrelation function
The PSD of a digital signal is given by:

14. PSD for Polar NRZ Signaling
Possible levels for the a’s : +A and -A

15. PSD for line codes
Unipolar NRZ
Polar NRZ
Bit rate: R=1/Tb

16. PSD for line codes Bit rate: R=1/Tb Unipolar RZ Bipolar RZ Manchester
NRZ
Bit rate: R=1/Tb