Digital communications

A.SANYSI RAO AMIE; M.Tech; MISTE; MIETE

Assoc. Professor Balaji Institute of Engineering & Sciences

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Transformation of Information to Signals

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Bandwidth

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Bit Rate and Bit Interval

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Corruption Due to Insufficient Bandwidth

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Objective To send information

•Reliability •As fast as possible

Constraints Rules of the GAME

•Limited transmit power •Limited Channel Bandwidth

In our control We get to DESIGN the

•Transmitter •Receiver

as long they follow the rules of the GAME.

Major Tools

•Signals & Systems •Probability Theory

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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

voltage.

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Bandwidth for Telephone Line

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Parallel Transmission

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Serial Transmission

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Asynchronous Transmission

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Synchronous Transmission

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Ideal pulse shapes.

Non ideal pulse shape.

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Core Concepts of Digital Communications

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Source of Information

Source Encoder

Channel Encoder

Modulator

Use of Information

Source Decoder

Channel Decoder

Demodulator

Channel Binary Stream

Elements of a Digital Communication System

Modulator

Demodulator

Modified Diagram of a Digital Communication System

Source of Information

Source Encoder

Encryptor

Channel

Channel Encoder

MUX

Use of Information

Source Decoder

Decryptor Channel Decoder

DE- MUX

From other Sources

To other Sources A.S.Rao

• 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 path.

• 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. A.S.Rao

• Digital signal storage is relatively easy and inexpensive.

• Reproduction with digital messages is extremely reliable without deterioration.

• The cost of digital hardware continues to halve every two or three years, while performance or capacity doubles over the same time period.

Disadvantages

• TDM digital transmission is not compatible with the FDM

• A Digital system requires large bandwidth.

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PCM System

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•Quantization process •Quantization Error •Mean Square Value of Quantization Noise •SNR of PCM system A.S.Rao

M S Q.E n S/N BW A.S.Rao

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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

2 4 6 8

2

4

6

-2

-4

-6

Input sample

Output sample

-2 -4 -6 -8

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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 nonlinearity.

•The process of compressing and expanding is called Companding.

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compression+expansion companding

)(ty)(tx )(ˆ ty )(ˆ tx

x

x

yCompress Uniform Qauntize

Channel Expand

Transmitter Receiver

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Telephones in US, Canada and Japan use -law Companding. (=255)

A-Law is used elsewhere to compress digital telephone signals.

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Digital Formats

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Differential PCM

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•PCM is powerful, but quite complex coders and decoders are required.

•An increase in resolution also requires a higher number of bits per sample.

•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. A.S.Rao

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. A.S.Rao

DM Transmitter

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DM Receiver

Limitations / Problems of DM system

•Slope over load error •Granular error (or) Hunting

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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 overload.

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.

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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.

M=2n

M- ary Signaling

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DIGITAL MODULATION

Input Binary data

Output Symbol/waveform

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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

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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.

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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

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ASK

FSK

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PSK

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QPSK

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8 PSK

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The 4-QAM and 8-QAM constellations

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Time domain representation for an 8-QAM signal

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16-QAM constellations

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Detection

• Coherent Detection • Non Coherent Detection

Bandwidth Efficiency

BW

BW

S

bBW

M

M

TB

B

rRateonTransmissiata

2

log

2

,BandwidthMinimum

,D

2

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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

Matched Filter

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)(2

)(

Im

0

tTxN

Kth

isFilterMatchedtheofresponsepulse

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Inter Symbol Interference

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• A sinc pulse has periodic zero crossings. If successive bits are positioned correctly, there will be no ISI at sampling instants.

Sampling Instants

ISI occurs but,

NO ISI is present at the sampling instants

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Raised Cosine Filter

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EYE DIAGRAMS

The eye diagram provides visual information that can be useful in the evaluation and troubleshooting of digital transmission systems. 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 A.S.Rao

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Eye Pattern formation

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Information Theory

• It is a study of Communication Engineering plus Maths.

• A Communication Engineer has to Fight with • Limited Power

• Inevitable Background Noise

• Limited Bandwidth

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bbib

bibbbi

KE

e

ERorSE

RSERES

easP b

/

varies

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

•Coding A.S.Rao

Information Sources:

•Analog Information Source

•Discrete Information Source

Information Measure

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” A.S.Rao

Let I(mK) the information content in the Kth message.

100)(

1)()(

10)(

kk

jKjk

Kk

PformI

PPformImI

PformI

2)()()()( jkjkjk mImImmImandmI

k

bkP

mI1

log)(

The quantity I(mk) is called the Self information of message mk. The self information convey the message is

PI

1log

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Why Coding?

• 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

Coding

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• Source Coding

• Channel Coding

Source Coding

• Shannon Fano Code

• Huffman Code

Channel Coding

• Linear Block Codes

•Cyclic Codes

• Convolutional Codes A.S.Rao

Algorithm. 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……..

Shannon Fano Source code

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Messages

Mi Pi No. Of

Bits Code

M1

M2

M3

M4

M5

M6

M7

m8

½

1/8/

1/8

1/16

1/16

1/16

1/32

1/32

0

1

1

1

1

1

1

1

0

0

1

1

1

1

1

0

1

0

0

1

1

1

0

1

0

1

1

0

1

Coding Procedure

1

3

3

4

4

4

5

5

0

100

101

1100

1101

1110

11110

11111

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HUFFMAN CODING

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SHANNON HARTLEY CHANNEL CAPACITY THEOREM

N

SBC 1log2

Channel Capacity with Infinite Bandwidth

SCLt

B44.1

B

C

S44.1

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