Communications and Networks (311SE) Course Work - B.Shakeal 4750820

7/22/2019 Communications and Networks (311SE) Course Work - B.Shakeal 4750820

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FACULTY OFENGINEERING AND COMPUTING

BACHELOR OF ENGINEERING (HONS)

IN

ELECTRICAL AND ELECTRONICS ENGINEERING

A311SE COMMUNICATIONS AND NETWORK

Course Work

STUDENT NAME : M.BADURDEEN SHAKEAL

STUDENT ID : 4750820

SUPERVISOR : Dr. ROHAN MUNASINGHE

SUBMISSION DATE : 2012.10.01


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PROJECT/ASSIGNMENT SUBMISSION ACKNOWLEDGEMENT SLIPName of Student: _________________________________ Student No: _____________________________

Home Address: __________________________________________________________________________

Date of Submission: _______________________________ Name of Tutor: LE LE YI

Program/ Module: Bachelor / A311SE (Communications & Networks)

Individual Assignment: Design based CAD/ Implementation Assignment

Received By: _________________________ Date: ___________________________________

Individual Projects (30%)

Marks

Learning OutcomeWeightage 1

stmarker

2nd

marker/moderator

Finalmark

Q1. Appraise multi-level digital modulationtechniques

Principle of operations of multilevel digitalmodulations

Principles of M_QAMmodulation technique

Parameters for Performance measurement of M-QAM modulation

Design selection and calculations for M_QAM

MATLAB simulation

Analysis/ discussion on Results

45%

3%

4%3%

11%14%10%

Q2. Apply the principles of error correction coding.

Principles of FEC coding Performance measurement parameters for FEC

coding

Principles of Hammingcoding and decoding Design selection and Calculations for Hamming

coding and decoding

MATLAB Simulation

Analysis / discussion on Results

45%

3%

3%3%

11%

15%10%

Quality and structure of report10%

Total Marks 100%

M.Badurdeen Shakeal 4750820

2012.10.01


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1stmarkers comment

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2nd

markers/ moderator comment

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Plagiarism Check

Turnitin checkCollusion check


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Page - i

Declaration of Originality

I Badurdeen Shakeal declare that this thesis is my own work and contains no material which has

been accepted for a degree or diploma by the University or any other institution, except by way

of background information and duly acknowledged in the thesis, and to the best of the my

knowledge and belief no material previously published or written by another person except where

due acknowledgement is made in the text of the thesis, nor does the thesis contain any material

that infringes copyright.

List of reference is given at the end of the assignment report using Coventry University Harvard

style referencing. This project is submitted in partial fulfilment of the requirements of the award

of Bachelor of Engineering (Hons) in Electrical & Electronic Engineering.


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Page - ii

Acknowledgment

First and foremost, I would like to thank to our Lecture Dr. Rohan Munasingheof this course

work, Mr. Duminda Wijesinghefor the valuable guidance, advice and supervising. He inspired

us greatly to work in this course work. His willingness to motivate us contributed tremendouslyto our course work. I also would like to thank Mr. Sujeewa Perera the librarian cum academic

support executive of Auston Institute of Management Ceylon for helping us with library

resources. Besides, I would like to thank the management of Auston Institute for providing us

with a good environment and facilities to complete this course work. Also, I would like to take

this opportunity to thank to the Coventry University for offering this program, computing course

work. It gave us an opportunity to learn about the operation of multilevel digital modulation and

forward error correction. Finally, an honorable mention goes to our families and friends for their

understandings and supports on us in completing this project. Without helps of the particular that

mentioned above, we would face many difficulties while doing this.


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A311SE Communications and Network

COVENTRY UNIVERSITY STUDENT ID: 4750820 Page 1

Contents

Abstract .................................................................................................................... 4

1.1 Motivation................................................................................................................................... 4

1.2 Problem statement and scope of project...................................................................................... 5

1.3 Methodologies............................................................................................................................. 5

1.4 Result and conclusions................................................................................................................ 5

Introduction ............................................................................................................. 6

2.1. Background.................................................................................................................................. 6

2.2. Objectives.................................................................................................................................... 6

2.3. Scope/limitation of project.......................................................................................................... 6

3. Literature Review ............................................................................................... 7

3.1 Principle of operations of multilevel digital modulations.................................................................. 7

3.2 Principle of operations of M-QAM modulation................................................................................ 8

3.3 Parameters for performance measurement of M-QAM modulation................................................ 11

3.4 Principles for Forward Error Correction (FEC) coding................................................................... 14

3.5 Principles for hamming coding and decoding................................................................................. 17

4 Design criteria and calculations ...................................................................... 22

4.1 Design selection, criteria for M-QAM modulation......................................................................... 22

4.2 Design calculations for M-QAM modulation.................................................................................. 23

4.3 Design selection / criteria for (n, k) hamming coding and decoding............................................... 25

4.4 Design calculations for (n, k) hamming coding and decoding........................................................ 26

5. MATLAB Programming .................................................................................. 30

5.3 MATLAB program for M-QAM digital modulation................................................................. 30

5.4 MATLAB program for (7, 4) hamming coding and decoding.................................................. 32

5.4.1. MATLAB code for (7.4) Hamming coding....................................................................... 32

5.4.2. MATLAB simulation code for hard decision decoding.................................................... 32

5.4.3. MATLAB simulation code comparison of Bit Error Rate (BER) for coded and uncoded

signals. 33

5.5 Detail simulation steps and procedures..................................................................................... 35

5.5.1. Detail simulation steps of 8-QAM modulation.................................................................. 35


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5.5.2. Detail simulation steps of Hamming coding...................................................................... 37

5.5.3. Detail simulation steps of hard decision decoding............................................................ 40

5.5.4. Detail simulation steps of Bit Error Rate (BER) Comparison........................................... 44

6. Critical Analysis /Discussion and comparison on results .............................. 45

6.1 Analysis, discussion and comparison on different simulation results of M_QAM modulation 46

6.2 Analysis, discussion and comparison on different simulation results of Hamming coding and

decoding................................................................................................................................................. 46

6.3 Theoretical interpretation and Verification................................................................................ 46

7. Conclusions ........................................................................................................ 47

References ..................................................................Error! Bookmark not defined.


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List of Figures, Tables and Equations

Figure 1 Diagram of multilevel modulation .................................Error! Bookmark not defined.

Figure 2 Dagram of QAM Modulaion ............................................................................................ 8

Figure 3 Dagram of QAM Demodulaion ........................................................................................ 9

Figure 4 Bandwidth efficiency diagram ....................................................................................... 13

Figure 5- FEC System Diagram (A.B.Carlson, 2001) .................................................................. 16

Figure 6- Hamming Distance counting cube ................................................................................ 17

Figure 7 Block diagram for 8-ary QAM modulation .................... Error! Bookmark not defined.

Figure 8 Constellation Diagram for selected 8-ary QAM Modulation ......................................... 24

Figure 9 Programming code in MATLAB simulation software for 8-QAM Digital Modulation

for the output of the signal together with related input binary signal ........................................... 35Figure 10 Result shown in MATLAB simulation software for 8-QAM Digital Modulation for

the output of the signal together with related input binary signal ................................................ 35

Figure 11 Result of MATLAB simulation show the output of the signal together with related

input binary signal ........................................................................................................................ 36

Figure 12 Programming code in MATLAB simulation software for (7, 4) hamming coding ..... 37

Figure 13 Result shown in MATLAB simulation software for (7, 4) hamming coding .............. 37

Figure 14 Programming code in MATLAB simulation software for (7, 4) hamming codes hard

decision decoding ......................................................................................................................... 40

Figure 15 Result Shown in MATLAB simulation software for (7, 4) Hard Decision decoding. . 40

Figure 16 MATLAB coding in MATLAB simulation software for comparison of Bit Error Rate

(BER) for coded and uncoded signals .......................................................................................... 44

Figure 17 Result Show in MATLAB simulation software for comparison of Bit Error Rate

(BER) for coded and uncoded signals. ......................................................................................... 44

Figure 18 Result on MATLAB for Selected hamming coding..................................................... 45

List of Tables

Table 1 Bit Allocation Table for 8-ary QAM Modulation ........................................................... 24

Table 2 Codeword table ................................................................................................................ 27

Table 3 Decoding Table (Syndrome) ........................................................................................... 29
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Abstract

1.1MotivationFirst of all the actual motivation of accomplishing this course work is to get wide range of

knowledge withinside the regarding telecommunication transmission. Over time, the world

remains enhancing and advancing around us, there is lots heart and soul and personas wanting to

alter points about all of us all in the field of communication.

But alternatively tiny success is attained with this scientific stride, that's a similar in all human

beings they have a tendency to reside and assist a lesser amount of effort and time and much

more efficiently and effectively. This particular course work continues to be emotively dedicated

to communication strategies. Because we are inside a fast growing globe, where it really is

called an international village for people to stay in the actual reduces costs of that technology.

We have to have huge and also intricate communication national facilities is usually to be used

where a couple of primary modulation schemes has been used and tested throughout technique

environment with regard to appropriate operate. Which may end up being QAM (Quadrature

Amplitude Modulation) modulation technique.

Currently the communication have come up with numerous facilities and so there are several

processes to discover in the diverse kind of modulation techniques. Also on that point currently

certainly there exist wise the actual communication will have numerous noise full express and

not able to use properly where there will be more errors because of having difficulty and thus

that individuals should use computer simulation program such as MATLAB as it is an Advanced

programing language additionally numerical processing environment. Its used to change matrix

and also plotting regarding features and information.

The main aim with this venture is always to clearly realize and theoretically assess each and

every problem given under. The initial would be the comprehension of QAM digital modulation

techniques as well as the design of the Hamming code and its particular error recognition

techniques.


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1.2Problem statement and scope of projectIn this very initial Question, believe taking amplitudes as well as phase angles regarding

provided M value to plot the constellation diagram. Since the course work states utilize

MATLAB simulation software to simulate design the actual MQAM digital modulation and

possess showing regulated output signal as well as associated input binary sign.

Withinside the second question, to begin with must find the Block code and using that discover

parity check matrix (H), generator matrix (G) as well as codeword table. then find the syndrom

table. Issue informs to utilize difficult decision technique and to replicate the design utilize

Matlab software. With this locate overacting hamming code and also decoding.

1.3MethodologiesThe strategy utilized first of all is the calculating just about almost most exact numbers as well

as variables and then finally stepping into MATLAB software for implementation as well as

running purposes, where the accuracy of mathematical computed data could possibly be tested.

Similarly thing about this course work focuses the building of the Hamming code using basic

theory after this portion has been completed. Also finally MATLAB software has been used here

for implementing this interrogation.

1.4Result and conclusionsBenefits in this course work would that most mathematical components could be elucidated and

graphically represented using MATLAB computing software simulation. The main results of

this particular task accomplishment a comprehensive understanding is actually acquired

whenever completing this particular course work.

When utilizing this MATLAB simulation software program in 1st case we are able to check the

accuracy and reliability from the plotting diagram and the determined solutions we all do. Inside

second difficulty furthermore we use MATLAB in order to be able for you to help imitate the

record and to confirm the accuracy. In any case when using this particular software we could

discover the graphical answer and comprehension of the subject nicely as we want to operate in

useful every day in the life.


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Introduction

2.1.BackgroundBackground of this course work is whenever we come to telecom it is not easier compared to we

all thought. As it associated with of procedure going through the senders and also devices.

Therefore, there should be ways to handle and also correct whenever transmitting signals are

usually incorrect so that you can have got perfect as well as quick communication. Thus,

Forward error correction [FEC] may be the great way to perform that kind of scenario and also

FEC coding were created not merely to detect yet correct errors in the communication to avoid

requirement for retransmission.

FEC is actually techniques are often charge in wireless transmission, exactly in which

retransmission is strategies tend to be highly unproductive as well as error rate might be large.

Consequently this really is gaining popularity through other error correction techniques.

2.2.ObjectivesIn this course work really aim is actually examine the particular calculations and also results

which receive utilizing MATLAB encoding. As well as reading good results expression about

the techniques utilized in these systems and getting good results knowledge in hard choice

method in hamming programming and also decoding. Consequently simulation and comparison

of obtained value of coded and uncoded signals.

2.3.Scope/limitation of projectWhile In the first chapter M value is given by the lecturer. So through the use of M value k value

can be determine. Then through which have to prepare the particular binary bit assignment table.

From then on need to pull the constellation diagram regarding of QAM modulation. Then Utilize

the MATLAB software that can simulate the answer. Despite the fact that QAM effectiveness

will be high it has many downsides in fact. A very important factor is always that is much more

prone minimizing degree of noise is necessary to move the actual signal to various places. Not

only must that hen QAM having amplitude aspects one-linearly be maintained.


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3. Literature Review

3.1 Principle of operations of multilevel digital modulations.

In order to be able to help first view the functioning of multilevel digital modulation must realize

first why digital modulation is used in the field of telecommunication and also researches in entireworld.

Especially in telecommunication field the entire transmission to be achievable there has to be a

possible transmission media in which the transmission is actually generated (sender) and may

travel for the meant destination had been throughout communication it is known as the receiver.

In individuals transmitting media with inside conversation there is certainly merely a static range

of frequencies which can be found with regard to transmission purpose, as this can be obtained

we're able to not really perhaps transmit in all frequencies this may be devastating, if your option

would be not necessarily identified and the date that we sent wouldn't be suitable for that channel.

A prosperous plan was found following considerable research is in which to improve any

transmitting signal based on the information which is give feed to as input data, this particular

alteration of the signal is named as modulation. This information that is modulated might be

received by the receiver and also the information that's in the signal could be retrieved because

the original data that has been encoded this is known as demodulation. (Sklar, 2001)

Figure 1 Block Diagram of Multilevel Digital Modulation


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3.2 Principle of operations of M-QAM modulation.

Before viewing of M-QAM (Multiple Quadrature Amplitude Modulation) modulation will realize

first the understanding of functioning of the (QAM) Quadrature Amplitude Modulation and

demodulation.

QAM modulation and demodulation.

Quadrature Amplitude Modulation is really a combination of Phase-Shift-Key (PSK) and

Amplitude-Shift-Key (ASK) modulation techniques. Additionally QAM can be a form of digital

modulation much like Phase-Shift-Key other than digital information is within the amplitude and

also phase of the transmitting carrier. It is possible to deliver 2 different signals simultaneously

on the same carrier frequency, through the use of two copies of the carrier frequency, one altered

through 900 with regards to the additionalIn this modulation each carrier is ASK modulated.

(Sklar, 2001)

The above mentioned figure 2 shows the actual QAM modulation scheme generally. The

particular input can be a flow associated with binary numbers coming to a rate of R bps. This kind

of supply will be converted into two separate bit streams. Withinside the diagram, top of the

stream is actually ASK modulated over a carrier regarding regularity fc only multiplying the bit

stream by the carrier. Therefore, a binary "0" is represented by the absence of the carrier wave

2-bit serial to

parallel

converter

-/2

Binary Input

D(t) R bps

d1(t)

R/2 bps

d2(t)

R/2 bps

Carrier

Oscillator

Phase

Shift

cos(2fct)

sin(2fct)

QAM signalOut

S(t)

+

+

Figure 2 Dagram of QAM Modulaion


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and a binary 1 is represented by the presence of the actual carrier wave at a continuous

amplitude.

This exact identical carrier wave is shifted simply by simply 900 as well as used for ASK

associated with the lower binary stream. Both modulated signals are added together and

transmitted.

The transmitted signal can be expressed as follows:

() () () () ()---------Equation 1If a couple of- level ASK is used, then each of the two streams can be in one of two states and the

combined stream could be in one of4 = 2 2 states. That is fundamentally QPSK. If four level

ASK is used (i.e. four different amplitude levels), then the combined stream can be in one of 16

= 4 4 states. Systems using 64 and even 256 states have been implemented. The greater the

number of states, the higher the data rate that is feasible within a given bandwidth. The higher the

number of states, the larger the potential error rate due to noise and attenuation.

-/2

QAM

signal in

s(t) R bps

d1(t)

R/2 bps

d2(t)

R/2 bps

Carrier

Oscillator

Phase

Shift

cos(2fct)

sin(2fct)

Low Pass Filter

Low Pass Filter

y1(t)= d1(t)/2

y2(t)= d2(t)/2

Figure 3 Dagram of QAM Demodulaion


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The above figure 2 shows the QAM demodulation scheme in general terms. The input is a stream of QAM

signal arriving at a rate of R bps. This stream is converted into two separate bit streams. Both upper and

lower part signal go through two separate Low Pass Filters.

Quadrature amplitude modulation is a modulation scheme which has digital and analogue

The mathematical description of the new modulated signal

() () ()

-----------Equation 2The level parameter for in-phase component and quadrature component are independent of each other for

all i. M-ary QAM is a hybrid form of M-ary modulation.

M-ary amplitude-shift keying (M-ary ASK)

If bi=0 for all i, the modulated signal si(t) of above equation is reduces to

() () ( )}--------Equation 3


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3.3 Parameters for performance measurement of M-QAM modulationAverage signal to noise ratio (SNR)

Signal-to-noise ratio is understood to be the power ratio between signal and the background noise.

The particular ideas regarding signal-noise ratio and energetic range tend to be closely connected.

Powerful variety measures the particular proportion between the strongest un-distorted

transmission channel on a route and the bare lowest discernable signal. Which usually for most

reasons will be the noise level. SNR actions the actual percentage in among an arbitrary signal

and noise.

SNR is normally taken up indicate the average signal-to-noise ratio, as it is feasible for

instantaneous signal-noise ratio proportions will be significantly different. The idea may berecognized as normalizing the particular noise level to a single (0 dB) and calculating how far the

transmission. (R.S., 2004)

------Equation 4Exactly in which P is typical power. Both transmission noise power must be assessed at the very

similar and equal points in a system, and also inside the exact identical system bandwidth. If the

transmission as well as the noises are usually assessed throughout the exact identical impedance,

then the SNR can be obtained by establishing the actual square of the amplitude voltage. (Tocci,

2007)

All the received power Pris in the modulating signal

Relationship of Eb/N0and SNR as follow.

-------------Equation 5


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Bit error probability

For a rectangular constellation, a Gaussian channel, and matched filter reception, the probability

of bit error P is expressed by.

Where L represents the number of amplitude levels in one dimension. We assume that a sequence

of log L (k) bits are assigned to an L-ary symbol using a Gray code.

Noise power spectral density

Eb/N0 is the ratio of signal energy per bit to noise power density per Hertz and it is standard

quality to measure for digital communication system performance.

Power (W) = Energy/time ( J/s)

Eb= STb--------------Equation 7

------------Equation 8(A.B.Carlson, 2001)

Signal power

The average signal power = A2/2 ----------------Equation 9

------------Equation 6


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Bandwidth requirements

Operating points for coherent quadrature amplitude modulation (QAM) is plotted in Figure

Of the modulations shown, QAM is clearly the most bandwidth efficient.

Figure 4 Bandwidth efficiency diagram (Sklar, 2001)


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3.4 Principles for Forward Error Correction (FEC) coding.

FEC

Two main categories of FEC codes are block code and convolutional code

Throughout telecommunication, information theory, and code principle, forward error correction

(FEC) of channel is a technique used for controlling errors in data transmission over unreliable or

noisy communication channels. The particular central idea is the sender scribes their massage in

a redundant way approach by utilizing a good error-correcting code (ECC). The actual United

States math wizard Rich Overacting developed this field in the nineteen forties as well as invented

the very first error-correcting code for Hamming (7, 4) signal in 1950. (Anon., 2009)

The redundancy permits the particular receiver in order to be able for you to help identify arestricted quantity of error that may take place around what it's all about, and sometimes to fix

these errors without retransmission. FEC gives the receiver the ability to appropriate errors

without resorting to the change route so that you can ask for retransmission of knowledge,

however at the expense of a fixed, increased forwards channel bandwidth. FEC is therefore

applied in circumstances where retransmissions are costly or impossible, for example one-way

communication links when broadcasting in order to be able for you to help several shower

receiver throughout multicast. FEC details are usually added mass storage devices to allow

recuperation associated with corrupted information, and is widely used in modems.

FEC digesting in the receiver could be placed on a digital bit stream or perhaps the particular

demodulation of your digitally modulated carrier. For the last option, FEC is an integral part of

the preliminary analog-to-digital conversion withinside the receiver. The Viterbi decoder tools

the soft-decision algorithm to demodulate digital information through an analog signal damaged

through noises. Several FEC coders also can produce bit-error rate (BER) signal transmission

which may be utilized since comments so that you can refine the particular analog getting

electronics. (Anon., 2009)

The utmost fragments of errors or of missing bits that may be corrected is determined by the

design of the particular FEC code, thus different forward error correcting codes are suitable for

diverse ailments.


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Two main principle type of FEC codes are

Block code Convolutional code

Block code

Error-correcting codes are employed to dependably transmit digital information over variable

connections and communication channel subject to channel noise. Each time transmitter needs to

transfer a possibly very long data stream using a block code, the particular transmitter breaks or

cracks the actual stream upwards in to piece of a few fixes size. Every such piece is called messageand also the procedure given by the actual block code encodes each massage individually right in

to a codeword, also referred to as the block poor obstruct rules. The particular transmitter next

transfers just about almost most blocks for the recipient, who is able to subsequently use some

decoding mechanism to recover the original communications from the probably damaged

received blocks. The particular performance and also success of the total transmitting depends

upon the parameters of the channel and the block code. (A.B.Carlson, 2001)

Convolution Code

Convolutional codes are used thoroughly in various applications to have trustworthy data

transmission, such as digital electronic video, radio, microwave mobile communication, and also

satellite communication. These types of codes in many cases are implemented in concatenation

using a hard-decision code, particularly Reed Solomon. Just before turbo codes, this kind of

improvements had been probably one of essentially by far the best efficient, returning best

towards the Claude Shannon limit. (Sklar, 2001)

Add redundant bits to a massage so that error can be detected and corrected

Rate of code is a measure of redundancy = ratio of massage bits to total bits


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Maybe effected on fixed length data blocks (block codes) or on a continuous data stream

(convolutional codes)

Figure 5- FEC System Diagram (A.B.Carlson, 2001)


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3.5 Principles for hamming coding and decoding.

Hamming distance

The number of symbol positions in which two code words vary is denoted as a Hamming distance,

d. e.g. 1001 and 1000 are separated by Hamming distance 1, while 1001 and 0110 are separated

by distance 4. Codes with larger minimum Hamming distance dmin are more powerful. Binary

words of the length n carrying only k information bits contain redundancy which, if properly

structured can provide. Redundancy for error detection and correction in an (n, k) code. The ratio

R is the code rate is k/n. (Tocci, 2007)

Hamming Distancecount

3-bit binary words arranged in 3-dimensional space on a cube. Minimum Hamming distance

between words is 1. Words 000 and 111 have distance 3 and represent EEC. Code rate is 1/3,

single errors can be corrected.

Example:

Then hamming distance is = 3

Figure 6- Hamming Distance counting cube


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The minimal Hamming distance between any two correct codeword is 3, and received words can

be correctly decoded if they are at distance at most one from the codeword that was transmitted

by the sender.

Hamming Distance = Minimum Weight

Parity Checks

We can add a parity bit to a word to ensure that it has a defined parity 1110 has odd parity (odd

number of 1s). A single error will then disturb the parity and thus be detected, this is the basis

for error correction coding. By introducing parity bits applied across subsets of the information

bit positions it is possible to both detect and correct errors the basis of error correction codes

(ECCs). The parity bits are sometimes mixed in with the information bits rather than attached at

the end of the code word.

Block Codes

A block code is a code that operates upon fixed-length blocks of information bits. In (n,k) block

codes each sequence of k information bits is mapped into a sequence of n(n >k). In order to

achieve high error correction and detection capability the code minimum distance and code rate

is should be large. Systematic block code is the block code which has the following structure

where: (A.B.Carlson, 2001)

First k elements are the same as the message bits, c=n-k bits are the check bits


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3.6 Performance measurement parameters for FEC coding.

Code rate

The Shannons theorem defined the code rate as the ratio of the data bits k to total bits n. Its

the measure of how much additional bandwidth is required to carry data at the same data rate as

without code

SNR

The actual SNR benefit indicates the number of energy required to obtain a specific BER price. Typically

a bigger SNR value results in lower BER. Programming obtain will be defined because the quantity of

enhancement as well as level of superior throughout SNR, whenever a particular programming structure is

employed. The normal way of discovering code acquire is to plot the actual BER versus SNR for equally

numbered and united nations touch pad program, (Tocci, 2007)

SNR calculation Equation

----------Equation 10

------------Equation 11


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Minimum Distance

The actual minimum distance provides all of us all a security program against noise and also attenuations.

This particular mechanism the minimal range in among code phrases can be utilized for problem diagnosis

and/or error a static correction. The actual fail-safe system regarding problem diagnosis, and or a static

correction capacity for a FEC are determined by just about the minimum distance of the FEC. This might

be worked out in two methods can be that we can help to eliminate the number of error corrections and or

raise the number of mistake detections or even the other way circular. This can be the hamming distance.

The hamming distance will be acquired by the bare lowest length between of two codewords. (R.S., 2004)

Minimum distance calculation equation

( ) ( ) ( ) { }

Coding gain

The coding gain defined as reduction in Eb/No(dB) to achieve a specific BER of and error

correcting coded system compared to encoded system using the same modulation

---------Equation 13

---------------Equation 14


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Error Detecting Capability

The maximum number of errors t that can be detected satisfies.

--------------Equation 15Error Correction Capability

The maximum number of guaranteed correctable errors per code word satisfies

Closure property of a code

The closure property describes that the sum of any two codewords in the space must yield a valid

codeword in the space.


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4 Design criteria and calculations

4.1 Design selection, criteria for M-QAM modulation

This is an 8-ary QAM

Block Diagram for 8-QAM transmitter

Bit Splitter

Q I C

2- to-4 Level

Converter

2- to-4 Level

Converter

Product

Modulator

Product

Modulator

Reference

Oscillator

Linear

Summer

Band pass

Filter

+900

Input Data

fb

fb/3

fb/3

fb/3

A Channel

B Channel PAM

PAM

8-QAM

Output

Sin wct

Figure 7 Block Diagram for given 8-ary QAM modulation


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4.2 Design calculations for M-QAM modulation

Calculations

Value of M=8, thus this is 8-ary QAM

Calculation of k using given value M

( )------------Equation 16

( )

In line with this QAM there are 8 signals to be allocate. Thus here 2 two different amplitudes and 4

different phases has been assigned.

Amplitude and phase allocation

1. Amplitude A1 = 1.5V,2. Amplitude A2 = 3.0V

Phase allocation

1. Phase 1 = 00,2. Phase 1 = 900,3. Phase 1 = 1800,4. Phase 1 = 2700


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Bit assignment table

Bit Assignment Output

Q I C Amplitude (v) Phase

0 0 0 1.5 0

0 0 1 3 0

0 1 0 1.5 90

0 1 1 3 90

1 0 0 1.5 180

1 0 1 3 180

1 1 0 1.5 270

1 1 1 3 270

Table 1 Bit Allocation Table for 8-ary QAM Modulation

Constellation Diagram this 8-QAM modulation

Symbol rate will be 1/3 of bitrate.

Y-axis

X-axis000

010

100

110

001

011

101

111

Figure 8 Constellation Diagram for selected 8-ary QAM Modulation


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4.3 Design selection / criteria for (n, k) hamming coding and decoding

Value for mprovided is 8

( )-----------Equation 17So value of n

Value of k Here number of check bit

By the determination from above equations the hamming code ( ) ()So here there are 4 data bits has been added with 3 parity bits to build a 7 bit codeword. So there

are 16 combination can be used for this 4 bit parity matrix. Those are 000, 001, 010, 011, 100,

101, 110, and 111.

Allocated Parity Equations


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4.4 Design calculations for (n, k) hamming coding and decoding

Construction of matrix algebra Parity Check Matrix

----------------Equation 18

Generator Matrix

-------------Equation 19

Codeword Calculation

For data sequence 0000

------Equation 20

For data sequence 0001


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Similarly codeword table is generated by possible codeword

Codeword Table

No. M1 M2 M3 M4 P1 P2 P3 Code weigh

0 0 0 0 0 0 0 0 0

1 0 0 0 1 0 1 1 3

2 0 0 1 0 1 0 1 3

3 0 0 1 1 1 1 0 4

4 0 1 0 0 1 1 0 3

5 0 1 0 1 1 0 1 4

6 0 1 1 0 0 1 1 4

7 0 1 1 1 0 0 0 3

8 1 0 0 0 1 1 1 4

9 1 0 0 1 1 0 1 4

10 1 0 1 0 0 1 0 3

11 1 0 1 1 0 0 1 4

12 1 1 0 0 0 0 1 3

13 1 1 0 1 0 1 0 4

14 1 1 1 0 1 0 0 4

15 1 1 1 1 1 1 1 7

Table 2 Codeword table

Minimum distance = Minimum code weight =

----------Equation 21

Error detecting capability

---------Equation 22


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Error correcting capability

--------Equation 23 Syndrome

Syndrome for e =0000000

Syndrome []

-----------Equation 24


[

]


[

]


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Similarly decoding table is generated by possible syndromes

Decoding Table

Error Pattern Syndrome

0000000 000

1000000 111

0100000 110

0010000 101

0001000 011

0000100 100

0000010 010

0000001 001

Table 3 Decoding Table (Syndrome)

Illustration of decoding

Massage is 1111, transmitted codeword is 1111111 and received codeword is 1011111

So e = 1011111 and s = 110

Correction is 1111111 and decoded massage is 1111.


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5. MATLAB Programming

5.3 MATLAB program for M-QAM digital modulationMATLAB programfor simulate the designed 8-ary QAM digital modulation in the simulationresult, output modulated signal together with related input binary signal

Input data Stream is 001011010000100101111110

format long;clcclear allM=8;data='001011010000100101111110';A1=1.5; A2=3;

f=2;t=linspace(0,1,900);time=[];Digital_signal=[];QAM_signal=[];

N=length(data)/log2(M);phase=[0 0 pi/2 pi/2 pi pi (3*pi)/2 (3*pi)/2];phase_data=[];fork=1:3:length(data)

phase_data=[phase_data bin2dec(data(k:k+2))+1];

endforkk=1:1:N

QAM_signal=[QAM_signal (phase_data(kk)==1)*A1*sin(2*pi*f*t + phase(1))+...

(phase_data(kk)==2)*A2*sin(2*pi*f*t + phase(2))+...(phase_data(kk)==3)*A1*sin(2*pi*f*t + phase(3))+...(phase_data(kk)==4)*A2*sin(2*pi*f*t + phase(4))+...(phase_data(kk)==5)*A1*sin(2*pi*f*t + phase(5))+...(phase_data(kk)==6)*A2*sin(2*pi*f*t + phase(6))+...(phase_data(kk)==7)*A1*sin(2*pi*f*t + phase(7))+...(phase_data(kk)==8)*A2*sin(2*pi*f*t + phase(8))];

time=[time t];t=t+1;

endt1=linspace(0,1/3,300);forjj=1:1:length(data)

Digital_signal = [Digital_signal (str2num(data(jj))==0)*zeros(1,length(t1))+...(str2num(data(jj))==1)*ones(1,length(t1))];

t1=t1+(1/3);endsubplot(2,1,2);

plot(time,QAM_signal,'.');title('8QAM Signal'); xlabel('time'); ylabel('Amplitude');axis([0 time(end) -8 8]);text(0.3,5.2,'\bf001'); %001text(1.3,5.2,'\bf011'); %011text(2.3,5.2,'\bf010'); %010text(3.3,5.2,'\bf000'); %000text(4.3,5.2,'\bf100'); %100


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text(5.3,5.2,'\bf101'); %101text(6.3,5.2,'\bf111'); %111text(7.3,5.2,'\bf110'); %110grid on;subplot(2,1,1);

plot(time,Digital_signal,'LineWidth',3);

title('Digital Input Signal'); xlabel('time'); ylabel('Amplitude');axis([0 time(end) 0 2]);grid on;text(0.3,1.3,'\bf001');%001text(1.3,1.3,'\bf011');%011text(2.3,1.3,'\bf010');%010text(3.3,1.3,'\bf000');%000text(4.3,1.3,'\bf100');%100text(5.3,1.3,'\bf101');%101text(6.3,1.3,'\bf111');%111text(7.3,1.3,'\bf110');%110


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5.4 MATLAB program for (7, 4) hamming coding and decoding5.4.1. MATLAB code for (7.4) Hamming coding%Simulation for encoding and decoding of a [7,4] Hamming code. The decoder

clearn = 7%# of codeword bits per blockk = 4%# of message bits per blockA = [ 1 1 1;1 1 0;1 0 1;0 1 1 ]; %Parity submatrix-Need binary(decimal combination of 7,6,5,3)

G = [ eye(k) A ]%Generator matrixH = [ A' eye(n-k) ]%Parity-check matrix

% ENCODER%msg = [ 1 1 1 1 ] %Message block vector-change to any 4 bit sequencecode = mod(msg*G,2)%Encode message

code(2)= ~code(2);

recd = code %Received codeword with error

5.4.2.MATLAB simulation code for hard decision decoding% DECODER%

syndrome = mod(recd * H',2)%Find position of the error in codeword (index)find = 0;forii = 1:n

if~finderrvect = zeros(1,n);errvect(ii) = 1;search = mod(errvect * H',2);ifsearch == syndrome

find = 1;index = ii;

endend

enddisp(['Position of error in codeword=',num2str(index)]);correctedcode = recd;correctedcode(index) = mod(recd(index)+1,2)%Corrected codeword%Strip off parity bitsmsg_decoded=correctedcode;msg_decoded=msg_decoded(1:4)


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5.4.3.MATLAB simulation code comparison of Bit Error Rate (BER) for codedand uncoded signals.

% Script for computing BER with Hamming (7,4) code and maximal% likelihood hard decision decoding

clearN = 10^6 ;% number of bits

Eb_N0_dB = [0:1:10]; % multiple Eb/N0 valuesEc_N0_dB = Eb_N0_dB - 10*log10(7/4);

h = [ 1 1 1 ; 1 1 0; 1 0 1; 0 1 1];ht = [h ;eye(3)];g = [eye(4) h];synRef = [ 5 7 6 3 ];

bitIdx = [ 7 7 4 7 1 3 2].';

foryy = 1:length(Eb_N0_dB)

% Transmitterip = rand(1,N)>0.5; % generating 0,1 with equal probability

% Hamming coding (7,4)ipM = reshape(ip,4,N/4).';ipC = mod(ipM*g,2);cip = reshape(ipC.',1,N/4*7);

% Modulations = 2*cip-1; % BPSK modulation 0 -> -1; 1 -> 0

% Channel - AWGNn = 1/sqrt(2)*[randn(size(cip)) + j*randn(size(cip))]; % white gaussian noise, 0dB variance

% Noise additiony = s + 10^(-Ec_N0_dB(yy)/20)*n; % additive white gaussian noise

% Receiver

cipHard = real(y)>0; % hard decision

% Hamming decodercipHardM = reshape(cipHard,7,N/4).';syndrome = mod(cipHardM*ht,2); % find the syndromesyndromeDec = sum(syndrome.*kron(ones(N/4,1),[4 2 1]),2); % converting the three bit syndrom to decimalsyndromeDec(find(syndromeDec==0)) = 1; % to prevent simulation crash, assigning no error bits to parity

bitCorrIdx = bitIdx(syndromeDec); % find the bits to correctbitCorrIdx = bitCorrIdx + [0:N/4-1].'*7; % finding the index in the arraycipHard(bitCorrIdx) = ~cipHard(bitCorrIdx); % correcting bitsidx = kron(ones(1,N/4),[1:4]) + kron([0:N/4-1]*7,ones(1,4)); % index of data bitsipHat = cipHard(idx); % selecting data bits

% counting the errorsnErr(yy) = size(find([ip- ipHat]),2);


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end

theoryBer = 0.5*erfc(sqrt(10.^(Eb_N0_dB/10))); % theoretical ber uncoded AWGNsimBer = nErr/N;

close allfiguresemilogy(Eb_N0_dB,theoryBer,'bd-','LineWidth',2);hold onsemilogy(Eb_N0_dB,simBer,'ms-','LineWidth',2);axis([0 10 10^-5 0.5])grid onlegend('theory - uncoded', 'simulation - Hamming 7,4 (hard)');xlabel('Eb/No, dB');ylabel('Bit Error Rate');title('BER for BPSK in AWGN with Hamming (7,4) code');


40/54



Figure 10Result shown in MATLAB simulation software for 8-QAM Digital

odulation for the output of the signal together with related input binary signal

5.5Detail simulation steps and procedures5.5.1.Detail simulation steps of 8-QAM modulation.Result of M-QAM digital modulation obtained by MATLAB simulations

Figure 9 Programming code in MATLAB simulation software for 8-QAM Digital Modulation

or the output of the signal together with related input binary signal


41/54



MATLAB simulation result. This figure 11 shows the output amplitude and phase combinations

related to the input Signal 001011010000100101111110

Figure 11 Result of MATLAB simulation show the output of the signal together with

related input binary signal


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5.5.2.Detail simulation steps of Hamming codingMATLAB simulation of hamming coding

Figure 12 Programming code in MATLAB simulation software for (7, 4) hamming coding

Figure 13 Result shown in MATLAB simulation software for (7, 4) hamming coding


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Result Obtain from MATLAB Simulation Software.

Hamming Code

n =

7

k =

4

G =

1 0 0 0 1 1 1

0 1 0 0 1 1 0

0 0 1 0 1 0 1

0 0 0 1 0 1 1

H =

1 1 1 0 1 0 0

1 1 0 1 0 1 0

1 0 1 1 0 0 1


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msg =

1 1 1 1

code =

1 1 1 1 1 1 1


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5.5.3.Detail simulation steps of hard decision decodingMATLAB simulation of hard decision decoding

Figure 14Programming code in MATLAB simulation software for (7, 4) hamming codes hard

decision decoding

Figure 15 Result Shown in MATLAB simulation software for (7, 4) Hard Decision decoding.


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Result Obtain from MATLAB Simulation Software for hard decision decoding.

n =

7

k =

4

G =

1 0 0 0 1 1 1

0 1 0 0 1 1 0

0 0 1 0 1 0 1

0 0 0 1 0 1 1


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H =

1 1 1 0 1 0 0

1 1 0 1 0 1 0

1 0 1 1 0 0 1

msg =

1 1 1 1

code =

1 1 1 1 1 1 1

recd =


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1 0 1 1 1 1 1

syndrome =

1 1 0

Position of error in codeword=2

correctedcode =

1 1 1 1 1 1 1

msg_decoded =

1 1 1 1


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5.5.4.Detail simulation steps of Bit Error Rate (BER) Comparison.MATLAB Simulations for comparison of Bit Error Rate (BER) for coded and uncoded signals.

Figure 16 MATLAB coding in MATLAB simulation software for comparison of Bit Error Rate

(BER) for coded and uncoded signals

Figure 17 Result Show in MATLAB simulation software for comparison of Bit Error Rate

(BER) for coded and uncoded signals.


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Graph for comparison of Bit Error Rate (BER) for coded and uncoded signals.

6. Critical Analysis /Discussion and comparison on results

In above (figure 18) the blue color curve shows the uncoded bit error rate and purple color curve

show the bit error rate for selected Hamming code.

Figure 18 Result on MATLAB for Selected hamming coding


51/54



6.1Analysis, discussion and comparison on different simulation results ofM_QAM modulation

As we know that QAM is a combination of ASK and PSK. Here we do with 8-QAM

modulation. For this 8-ary we can allocate different combinations like

Can be taken+ Single amplitude and 8 different phases+ Two amplitude and 4 different phases+ Four amplitude and 2 different phases+ Eight amplitude and single phase

According to the allocation of amplitude and phase constellation diagram is varying.

6.2Analysis, discussion and comparison on different simulation results ofHamming coding and decoding

According to the allocation of m value the hamming code is coming deferent. Here we allocate 3

for m value. We can see here that according to the allocation of parity equation the hamming

code simulation is coming different and results are obtain also different.

As well as consistent with parity equation the parity check matrix and generator matrix is

changing. And also the result of MATLAB simulation is changing.

Also we can see here when we changing the parity equation the coded BER (Bit Error Rate) alsoaltering habitually.

6.3Theoretical interpretation and VerificationIn both situation (QAM and Hamming code) the MATLAB simulation shows equality of actual

calculation result. So theoretically both section can be design cad based implementation using

MATLAB simulation software.


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7. Conclusions

We will go over the particular computer simulation results. The actual hamming code is a seo'ed

bitwise FEC for that Gaussian channel. Numerous transmission schemes include broke errors

exactly in which they will happen really withinside surrounding bits. The actual channel inbuilt

dynamics at times is employed to correct short burst problems. The channel interleaves attempts

to set aside burst open errors arbitrarily within a obstruct of data where they may be remedied by

way of a appropriate haphazard FEC at the shower radios finish, for instance Hamming code

rule. In this training we view such a situation. The key portion is that the calculation of BER

exactly in which this exhibits people the mistake rate from particular Eb/No. wherever this

demonstrates a great uncoded program provides little error rate at commence where Eb/no tend

to be small. However, if the data movements away a sizable power must keep up with the

problem rate do i think the particular numbered program.

More than I'm able to point out which this QAM modulation is very important since it could be

followed in to numerous engineering with the present. As an example, when we all work with a

cable system the actual slandered of QAM modulation, its extensive for signal digesting. Here

we have examined the actual performance regarding 8-QAM modulation. Here we can easily

transmit more data rate actually. To ensure that we could view the QAM passage getting much

far greater overall efficiency than PSK and have transitions because when using dull program

rule methods this can possess a lot more performances. In this syllabus we understood how the

QAM is a combination of PSK and ASK modulations. Anyhow the QAM could be exact

identical in order to be able for you to help PSK in the event the electronic digital camera

information wasnt possessing 2 service providers.

The actual acting signal can be referred to in array form with creator matrix as well as parity

check matrix. We need to calculate syndromes with regard to problem examining. In fact, when

a legitimate codeword will be grow from the examine array the particular symptoms comes zero.

Each time a codeword multiply along together using examine enclosure and also arriving non-

zero affliction this means there is a error. All solitary touch mistakes could be remedied and all

two-bit mistakes may be recognized.


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The main advantage of forward error correction coding can it be needs a feed back. Yet its bad

for multicast. In any case that's appropriate only for a few programs. This kind of FEC has a

proven way tranny and avoid multicast problems. Anyway its computationally pricey as well as

over-transmission


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References

A.B.Carlson, 2001. Communication System, an Introduction to signals and nise in electrical

communication.. 4th ed. s.l.:Mc Graw-Hill.

Anon., 2009. Radio-Electronics.Com. [Online]

Available at: http://www.radio-electronics.com/info/rf-technology-design/pm-phase-

modulation/8qam-16qam-32qam-64qam-128qam-256qam.php

[Accessed 25 09 2012].

R.S., D., 2004. In: Digital Transmission Systems. s.l.:s.n.

Sklar, B., 2001. Digital Communications, Fundamentals of Applications. 2nd ed. s.l.:Pearson Education.

Tocci, 2007. In: 1. Edition, ed. Digital System. s.l.:Prentice Hall of India, p. 80.

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