1. Digital Communications
Objectives
To describe a binary digital transmission system
To explain intersymbol interference
To show how an eye diagram is produced and explain its significance for system performance assessment
To show the pulses with zero intersymbol interference
To introduce the condition for zero intersymbol interference
To introduce the term “error probability”
To introduce the concept of error control coding
To introduce the concept of line coding and to provide illustrations of some practical line codes
To study digital carrier modulation schemes

2. Digital Communications
Recall that
PAM is the simplest pulse modulation system, and can be
used to get a complete digital system.
PAM signals  quantized  coded  PCM signal
PCM signals consist of binary digits, i.e. a string of 1’s and 0’s.
These binary digits are then transmitted over the transmission
channel
 digital transmission

3. Digital Communications
Binary digital transmission system
When the signal arrives at the output of the channel, it is
attenuated due to the loss and distorted due to limited bandwidth of the channel
The distortion can be partially corrected by the use of an equalizer.

4. Digital Communications
Equalization
A method of signal recovery is to use a filter that has a transfer function which is the reciprocal of the channel transfer function Q()
So that the output spectrum G0() = G()Q()Heq() becomes G()/T. This technique of correcting the frequency response of a system for a known distortion is called equalization.

5. Digital Communications
Equalization

6. Digital Communications
Binary digital transmission system

7. Digital Communications
Binary digital transmission system
Threshold device can restore the original signal, but the timing of the transitions may be irregular.
Causes of irregularity:
transition time varies with different transmission channels
2. threshold circuit may be corrupted by the noise
Thus, a clock waveform is extracted from the signal and used to retime the data.

8. Digital Communications
Intersymbol Interference
In practice, the digital pulses are not perfectly rectangular and
the transmission medium is neither perfectly linear nor
distortionless (because it has limited bandwidth).
A transmission channel has only limited bandwidth
 a small portion of signal spectrum is suppressed.
 signal spectrum distortion
 spreading of signal pulse (dispersion).
Spreading of a pulse beyond its interval causes it interferes
with neighboring pulses  intersymbol interference (ISI).

9. Digital Communications
Intersymbol interference

10. Digital Communications
Is it is possible to obtain zero ISI with limited channel bandwidth?
Condition for zero intersymbol interference (ISI)
If the signal shape is p(t), then p(t) must satisfy
p(0) = non-zero constant
p(nT) = 0, when n  0.
What kind of pulse shape satisfies the condition for zero ISI?

11. Digital Communications
However, it is virtually impossible to achieve this
kind of pulse shape in practice, as it is the impulse
response of an ideal lowpass filter.

12. Digital Communications
Both the intersymbol interference and noise may cause
errors, and hence affect the system performance.
How to evaluate the combination effect of noise and
intersymbol interference on overall system performance?
--- Use an eye pattern (eye diagram).
The eye pattern is the synchronized superposition of
all possible signal patterns obtained in a particular
signal interval.

13. Digital Communications
The eye pattern (eye diagram)

14. Digital Communications
The interior region of the eye pattern is called the eye
opening. (Eye opening is also the timing error allowed
on the sampler at the receiver)
Little ISI, little noise, little jitter  more open eye
An eye pattern provides useful information about the system performance.

15. Digital Communications
The width of the eye opening defines the time interval
over which the received signal can be sampled without
error from ISI.
(The best sampling time: when the vertical opening of
the eye is the largest)
The height of the eye opening, at a specified sampling
time, defines the system noise margin
The slope of the open eye indicates the sensitivity to the
timing error.

17. Digital Communications
Probability of error in transmission
In a binary digital communication system, the two
levels (“1” and “0”) may be represented by
A & 0 (unipolar binary signal) or
A & - A (polar binary signal)
In a polar binary signal transmission using pulse p(t), assume that the binary levels at the receiver are - A and A. The observed waveform y(t) contains random noise n(t), so that
y(t) = p(t) + n(t)

18. Digital Communicatins
At a given time t1, the possible receiver inputs are
A + n(t1) (signal present)
or - A + n(t1) (signal absent)
The detection threshold is 0, i.e.
if the sample value > 0, the digit is detected as “1”;
if the sample value < 0, the digit detected as “0”.
There is a probability that the noise amplitude > signal amplitude,  the error occurs when A + n(t1) is negative or – A + n(t1) becomes positive.

19. Digital Communications
Distribution of signal + noise

20. Digital Communications
Normally, the noise waveform has a Gaussian probability density
function (pdf)
where  is the rms value of the noise amplitude.
The probability of a one being interpreted as a zero (error):
The probability of a zero being interpreted as a one (another error):

21. Digital Communications
The total error probability is given by
Pe = P(1) P(01) + P(0) P(10)
where P(1) is the probability of a one being sent, and P(0) is that for a
zero. Usually ones and zeros are equally likely, so
P(0) = P(1) = ½.
Substituting x = (y + A)/, and x = (y – A)/ respectively,
we get
where T(A/) is known as the Gaussian tail function (sometimes
called the complementary error function).

22. Digital Communications
Thus,
Its values are given in tabular form in most mathematical
handbooks. Alternatively, it is given in graph form as a
function of the voltage SNR.
A standard norm for Pe is 10-9, that is, if the transmission
rate is 1 Gbit/s, there will be, on average, one error every
second.

24. Digital Communications
In binary PCM, each sample of the signal is represented by a codeword of, say, k bits. These bits are transmitted.
Receiver is used to recognize each codeword in order to reconstruct the samples, but errors may occur in the transmission as a result of noise.
Ways to improve the reliability:
to increase the signal-to-noise ratio.
to use appropriate coding.

25. Digital Communications
Coding for digital transmission
Several techniques of coding for digital transmission
will be discussed
source coding
error control coding
line coding

26. Digital Communications
Source Coding
Concerning with how should source messages be represented using the minimum number of bits.
Example: Encoding English text
Seven bit ASCII (American Standard Code for Information Interchange) code
Character Binary code Character Binary code
Space A a

28. Digital Communications
Error control coding
In error control coding, the extra digits are introduced, in order
to detect the presence of errors in the received pattern.
Parity checks
Sum check

29. Digital Communications
Row and column parity check

30. Digital Communications
Line Coding
The digital data need to be coded into electrical pulses
for the purpose of transmission over the channel. This
process is called line coding or transmission coding.
There are two major categories of line codes:
return-to-zero (RZ), and
nonreturn-to-zero (NRZ).
With RZ coding, the waveform returns to a zero-volt
level for a portion (usually half) of the bit interval.

31. Digital Communications
Line coding is used to match the digital signal to the
physical characteristics of the channel (e.g. zero dc
content) and facilitate synchronization at the receiver.
a communication channel should not transmit dc components, as it is the waste of signal power.
In order to maintain synchronization, there should be enough timing information built into the code so that the clock signal can be easily exacted. A long series of binary 1s and 0s should not cause a problem in time recovery.

32. Digital Communications
Unipolar code (on-off code)
A “1” is transmitted by a pulse and a “0” is transmitted by no
pulse.
Polar code
“1” is transmitted by a positive pulse p(t) and “0” is transmitted
by a negative pulse – p(t).
Bipolar code
“0” is encoded by no pulse and “1” is encoded by a pulse p(t)
or – p(t), depending on whether the previous “1” is encoded
by p(t) or – p(t). In short, pulse representing consecutive 1’s
alternate in sign. This format has zero dc level (assuming an
equal number of 1s and 0s).

33. Digital Communications

34. Digital Communications
The nonreturn-to-zero (NRZ) format is disadvantages because
it has a dc component and does not allow for self-clocking.
The NRZ-bipolar (NRZ-B) format eliminates the dc component
(assuming that an equal number of 1s and 0s occur) but it is
also not self-clocking.
The polar return-to-zero (RZ) format includes clock
information, has zero dc level (again, for equal numbers of 1s
and 0s), but has three voltage levels (for bipolar).

35. Digital Communications
Manchester code
A “1” is represented by a “1” level during the first half-bit interval, then shift to “0” level for the latter half-bit interval;
a “0” is indicated by the reverse representation.
Manchester code uses a level transition of one direction or the
other in the middle of every bit interval. This provides the
receiver with clocking information and produces a zero dc
level even if the 1s and 0s are not equal.

36. Digital Communications
The output of a PCM system is a string of 1’s and 0’s.
If they are transmitted over the transmission medium
such as the copper wire, they can be directly
transmitted as two voltage levels + V and – V, if a
polar code is adopted.
This is baseband digital transmission, the signals are
transmitted at their baseband frequency.

37. Digital Communications
If digital signals are to be transmitted over a
bandpass channel by use of high frequency carrier
wave such as signal transmission through space using
antenna, some form of modulation has to be used.
This is referred to bandpass digital transmission.

38. Digital Communications
Digital carrier modulation
There are three basic forms of digital modulation,
corresponding to AM, FM and PM are known as
amplitude-shift keying (ASK), frequency-shift
keying (FSK), and phase-shift keying (PSK), in which
the amplitude, frequency or phase of the sinusoidal
carrier is switched between either of two values
corresponding to a 1 or a 0.

40. Digital Communications
Amplitude Shift Keying (ASK)
In ASK, the modulated signal can be expressed as
Note that the modulated signal is still an on-off signal.
Thus, ASK is also known as on-off keying (OOK).

41. Digital Communications
Frequency Shift Keying (FSK)
In FSK, the modulated signal can be expressed as

42. Digital Communications
Phase Shift Keying (PSK)
In PSK, the modulated signal can be expressed as

43. Digital Communications
Digital carrier demodulation
The detection of digital carrier modulation systems is
virtually identical to that of analog modulation
systems, i.e. the coherent demodulation method is used.
OOK signals can be demodulated also by using an
envelope detector.

45. Questions (Digital Communications)
What is intersymbol interference? How is it generated?
What is eye diagram? What is its application?
What pulse shape has zero intersymbol interference?
What is the condition for zero intersymbol interference?
How are the two levels, “1” and “0”, represented in unipolar binary signal and in polar binary signal respectively?
What is the main advantage of source coding?
How bit streams are electrically represented in communication systems?
What are suitable methods to transmit PCM signals through space using antenna?

46. Exercise Problems (Digital Communications)
1. A digital transmission system employs a signal element waveform at the input to the decision circuit given by
p(t) = (1 – cos2t/T) / 2(t/T)2
Show that this provides zero ISI for a binary signalling rate of 1/T bits/s.

47. Exercise Problems (Digital Communications)
2. Consider a source which produces message based on three symbols: A, B, C. The symbols are found to occur, on average, with relative frequencies A = 0.5, B = 0.25, C = It is required to encode messages in a binary format; two coding schemes are proposed:
Scheme1: A = 01, B = 10, C = 11
Scheme2: A = 1, B = 01, C = 00
Show that, on average, a smaller number of bits per message are required for scheme 2 than for scheme 1.

48. 3. (a) The overall transfer function of a transmission medium is given as Ha(w). The inverse Fourier transform of this function is
If the sequence of pulses, shown below, is to be transmitted through the
medium given above, discuss whether there will be any possibility of
error due to intersymbol interference at the receiver. Explain. (Hint:
there is an inverse time-bandwidth relationship, i.e. B ~ 1 /τ, whereτis
pulse duration)
(b) If we now send the same sequence of pulses through another transmission medium which has the transfer function Hb(w) shown below, will there be intersymbol interference? Explain.