Corruption Due to Insufficient Bandwidth
Objective To send information
•As fast as possible
Constraints Rules of the GAME
•Limited transmit power
•Limited Channel Bandwidth
In our control We get to DESIGN the
as long they follow the rules of the GAME.
•Signals & Systems
Analog versus Digital
It is harder to separate noise from an analog signal than it is to
separate noise from a digital signal.
Noise in a digital signal. You can still discern a high voltage from a low
Core Concepts of
Elements of a Digital Communication System
Source of Source Channel
Information Encoder Encoder
Binary Stream Channel
Use of Source Channel
Information Decoder Decoder
Modified Diagram of a Digital Communication System
From other Sources
Source of Source Channel
Encryptor MUX Modulator
Information Encoder Encoder
Use of Source Channel DE-
Information Decoder Decoder MUX
To other Sources
• Can withstand channel noise and distortion much better as long
as the noise and the distortion are within limits.
• Regenerative repeaters prevent accumulation of noise along the
• Digital hardware implementation is flexible.
• Digital signals can be coded to yield extremely low error rates,
high fidelity and well as privacy.
• Digital communication is inherently more efficient than analog in
realizing the exchange of SNR for bandwidth.
• It is easier and more efficient to multiplex several digital signals.
• Digital signal storage is relatively easy and inexpensive.
• Reproduction with digital messages is extremely reliable without
• The cost of digital hardware continues to halve every two or
three years, while performance or capacity doubles over the
same time period.
• TDM digital transmission is not compatible with the FDM
• A Digital system requires large bandwidth.
Many signals such as speech have a nonuniform distribution.
– The amplitude is more likely to be close to zero than to be at higher levels.
Nonuniform quantizers have unequally spaced levels
-8 -6 -4 -2 2 4 6 8
Companding in PCM
•Non-uniform quantizers are expensive and difficult to make.
•An alternative is to first pass the speech signal through a non
linearity before quantizing with a uniform quantizer.
•The non linearity causes the signal amplitude to be compressed. So
the input to the quantizer will have a more uniform distribution.
•At the receiver, the signal is expanded by an inverse to the
•The process of compressing and expanding is called Companding.
x(t ) y (t ) ˆ
y (t ) ˆ
Compress Uniform Qauntize Expand
Transmitter Channel Receiver
•PCM is powerful, but quite complex coders and decoders are
•An increase in resolution also requires a higher number of bits per
•The Delta Modulation is the most economical form of Digital
Communication System since it requires only one bit per sample
(either low pulse or high pulse) transmitted through the line.
•Delta Modulation uses a single-bit PCM code to achieve digital
transmission of analog signals.
•Normally Sampled at high rate.
When the step is decreased, ‘0’ is transmitted and if it
is increased, ‘1’ is transmitted.
Delta Modulation: Unique Features
1. No need for Word Framing because of one-bit code word.
2. Simple design for both Transmitter and Receiver.
Limitations / Problems of DM system
•Slope over load error
•Granular error (or) Hunting
Slope overload - when the analog input signal changes at a faster
rate than the DAC can maintain. The slope of the analog signal is
greater than the delta modulator can maintain and is called slope
Granular noise - It can be seen that when the original analog input
signal has a relatively constant amplitude, the reconstructed signal
has variations that were not present in the original signal. This is
called granular noise. Granular noise in delta modulation is
analogous to quantization noise in conventional PCM.
M- ary Signaling
Multiple Signal Levels:
Why use multiple signal levels?
We can represent two levels with a single bit, 0 or 1.
We can represent four levels with two bits: 00, 01, 10, 11.
We can represent eight levels with three bits: 000, 001,
010, 011, 100, 101, 110, 111
Note that the number of levels is always a power of 2.
GOALS OF MODULATION TECHNIQUES
• Low cost and ease of implementation
• Low carrier-to-co channel interference ratio
• Low-Cost/Low-Power Implementation
• High Power Efficiency
• High Bit Rate
• High Spectral Efficiency
Bit Rate Vs Baud Rate
Bit rate is the number of bits per second. Baud rate is the number of
signal units (symbols) per second. Baud rate is less than or equal to
the bit rate.
Modulation Units Bits/Baud Baud rate Bit Rate
ASK, FSK, 2-PSK Bit 1 N N
4-PSK, 4-QAM Dibit 2 N 2N
8-PSK, 8-QAM Tribit 3 N 3N
16-QAM Quadbit 4 N 4N
32-QAM Pentabit 5 N 5N
64-QAM Hexabit 6 N 6N
128-QAM Septabit 7 N 7N
256-QAM Octabit 8 N 8N
• Coherent Detection
• Non Coherent Detection
Data Transmission Rate , rb
M inimum Bandwidth, B
log 2 M
The ultimate task of a receiver is detection, i.e. deciding between
1’s and 0’s. This is done by sampling the received pulse and
making a decision
Matched filtering is a way to distinguish between two pulses
with minimum error
Im pulse response of the Matched Filter is
h(t ) x(T t )
• A sinc pulse has periodic zero crossings. If successive bits
are positioned correctly, there will be no ISI at sampling
ISI occurs but,
NO ISI is present at the
The eye diagram provides visual information that can be useful
in the evaluation and troubleshooting of digital transmission
It provides at a glance evaluation of system performance and
can offer insight into the nature of channel imperfections,
Top: Undistorted eye diagram of a band limited digital signal
Bottom: Eye diagram includes amplitude (noise) and phase (timing) errors
• It is a study of Communication Engineering plus
• A Communication Engineer has to Fight with
• Limited Power
• Inevitable Background Noise
• Limited Bandwidth
P varies as e KEb
S i Eb Rb Eb Si / Rb
Eb S i or Rb Eb
Hartley Shannon has shown that
“If the rate of information from a source does not exceed
the capacity of a given communication channel, then there exists
a coding technique such that the information can be transmitted
over the channel with arbitrary small frequency errors, despite
the presence of noise.”
Information theory deals with the following three basic concepts:
•The measure of source information
•The information capacity of a channel
•Analog Information Source
•Discrete Information Source
Consider two Messages
A Dog Bites a Man High probability Less information
A Man Bites a Dog Less probability High Information
Information α (1/Probability of Occurrence)
The basic principle involved in determining the information
content of a message is that “the information content of a
message increases with its uncertainty”
Let I(mK) the information content in the Kth message.
I ( mk ) 0 for PK 1
I ( mk ) I ( m j ) for PK Pj 1
I ( mk ) 0 for 0 Pk 1
I (mk and m j ) I (mk m j ) I (mk ) I (m j ) 2
I (mk ) log b
The quantity I(mk) is called the Self information of message mk.
The self information convey the message is I log
• to achieve reliable data communication
• to achieve reliable data storage
• to reduce the required transmit power
• to reduce hardware costs of transmitters
• to improve bandwidth efficiency
• to increase channel utilisation
• to increase storage density
Shannon Fano Source code
Step 1: Arrange all messages in descending order of probability.
Step 2: Divide the Seq. in two groups in such a way that sum of
probabilities in each group is same.
Step 3: Assign 0 to Upper group and 1 to Lower group.
Step 4: Repeat the Step 2 and 3 for Group 1 and 2 and So on……..