ABSTRACT
Error correction codes are widely used in almost all digital systems as they provide a method for
dealing with the unknown, noise. This research has investigated the performance of error
correction codes in wireless communication systems with the use of MATLAB. The error
correction code employed was the convolution error correction codes. The performance of the
codes were evaluated based on key performance indicators like gain, Bit Error Rate (BER) e.t.c.
by transmitting randomly generated data through a Gaussian channel. For the verification of
proposed approach, computer simulation results are included. The results showed a comparison
of the performance of the convolution codes (with different code rates) in terms of their BER
performance. Based on the results of the plots, up to 70% and 74% improvement on coding
gains were achieved between reference points of 10
-2
and 10
-4
respectively for the two code rates
(1/2 and 1/3) used. The results also showed that with the BER decreased, the coded system can
transmit data signals with at least 3dB less power thus making the performance of the coded
system better than the uncoded system.
TABLE OF CONTENTS
TITLE PAGE……………………………………………………………………………………………………..i
DECLARATION……………………………………………………………………………………………….iii
CERTIFICATION ……………………………………………………………………………………………..iv
DEDICATION……………………………………………………………………………………………………v
ACKNOWLEDGEMENTS…………………………………………………………………………………vi
ABSTRACT………………………………………………………………………………………………………vii
CHAPTER ONE
INTRODUCTION ……………………………………………………………………………………………..1
1.1 GENERAL INTRODUCTION……………………………………………………………………….1
1.2 MOTIVATION…………………………………………………………………………………………….3
1.3 STATEMENT OF PROBLEM……………………………………………………………………….4
1.4 SIGNIFICANCE OF RESEARCH …………………………………………………4
1.5 OBJECTIVES OF THE STUDY……………………………………………………5
1.6 THESIS OUTLINE………………………………………………………………………………………..6
CHAPTER TWO
LITERATURE REVIEW AND THEORETICALBACKGROUND……………………7
2.0 LITERATURE REVIEW……………………………………………………………7
2.1 SHANNON LIMIT…………………………………………………………………..9
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2.2 ERROR CORRECTING CODES …………………………………………………..10
2.3 ERROR-CORRECTION CODE SELECTION……………………………………..11
2.4 TYPES OF ERROR CORRECTION CODES……………………………………….12
2.4.1 BLOCK CODES.…………………………………………………………………..12
2.4.2 CONVOLUTION CODES…………………………………………………………13
2.5 PROPERTIES OF CONVOLUTION CODES……………….……………………..14
CHAPTER THREE
DESIGN METHODOLOGY…………………………………..……………………….19
3.0 INTRODUCTION…………………………………………………………………..19
3.1 IMPLEMENTATION OF CODES…………………………………………………19
3.1.1 ENCODER REPRESENTATION………………………………………………..20
3.1.2 ENCODER STRUCTURE………………………………………………………..20
3.1.3 DECODING CONVOLUTIONAL CODES………………………………………22
3.2 PERFORMANCE MEASURE………………………………………………………23
3.3 PERFORMANCE ANALYSIS……………………………………………………..26
3.4 SIMULINK BLOCKS………………………………………………………………29
CHAPTER FOUR
RESULTS AND ANALYSIS………………………………………………………………………………33
4.0 SIMULATION RESULTS…………………………………………………………..33
4.1 RESULT DISCUSSION……………………………………………………….……34
4.2 SIMULATION PLOTS……….……………………………………………………..35
4.3 SIGNIFICANCE OF RESULT……………………………………………….………38
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CHAPTER FIVE
SUMMARY, CONCLUSION AND RECOMMENDATIONS……………………….39
5.1 INTRODUCTION..……………………………………..…………..……..……….39
5.2 SUMMARY….……………………………………………………..……………….39
5.3 LIMITATION…………………………………………….…..…………………….39
5.4 CONCLUSION……………………………………………………………………..40
5.5 RECOMMENDATIONS FOR FURTHER WORK………………………………….40
REFERENCES……………………………………..…….…………………………….42
APPENDIX A……………………………………………..…………………………….46
APPENDIX B……………………………………………………………………………50
CHAPTER ONE
INTRODUCTION
1.1 BACKGROUND INFORMATION
The last thirty years have seen a dramatic change in the way communication is achieved around the
world. Wireless communication has evolved from being an expensive and rare technology for the few in
the 70’s, to becoming a widespread and economical means for facilitating domestic, commercial, as well
as public service communications. One of the major reasons for the continuous growth in the use of
wireless communication is its increasing ability to provide efficient communication links to almost any
location, at constantly reducing costs with increasing power efficiency (Jemibewon, 2000).
Wireless communication is one of the most active areas of technological development. This
development is being driven primarily by the transformation of what has been a medium for supporting
voice telephony into a medium for supporting other services such as transmission of video, images, text,
and data e.t.c. (Wang and Poor, 2003). Basically, a communication system deals with information or
data transmission from one point to another (Du and Swamy, 2009). Over the years, there has been a
tremendous growth in digital communications especially in the fields of cellular, satellite, and computer
communications. In these communication systems, the information is represented as a sequence of
binary bits. The binary bits are then mapped (modulated) to analog signal waveforms and transmitted
over a communication channel. The communication channel introduces noise and interference to
corrupt the transmitted signal. At the receiver end, the channel corrupted transmitted signal is mapped
back to binary bits. The received binary information is an estimate of the transmitted binary information
(Huang, 1997). Normally, during signal transmission through noisy channels, errors can occur on the
received data. Bit errors may result due to this transmission and the number of bit errors depends on
the amount of noise and interference in the communication channel. These errors can be detected and
corrected using coding techniques (Huang, 1997). Noise is any undesired signal in a communication
circuit. Noise can also be unwanted disturbances superimposed on a useful signal, which tends to
obscure its information content. There are many varieties of noise; however, the three general types of
noise can be categorized as follows:
1) Gaussian noise is usually not dependent on time, meaning that it is random and not
systematically planned. The amplitude of the frequency can vary, making a crackling notation or
sound. Some examples of Gaussian noise can include splashing in a tank or unplanned
interruption in a sensing device.
2) Drift noise is correlated to time, and has random movement. Examples of drift noise can
include fouling or catalyst decay.
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3) Shot noise may be defined as sporadic and short bursts of noise, in which the amplitude is
similar among the bursts of noise. Examples of shot noise include partial clogging or jamming in
the process in which the same amplitude will be seen by the noise whenever the clogging or
jamming in the process occurs.
A sample communication system is shown in Figure 1.1
Figure 1.1: A
sample
communication
system
The information source is where the message originates and the destination is where it is received.
(Saha, 2003). Wireless communications encompasses various types of fixed, mobile, and portable twoway
radios, cellular telephones, personal digital assistants (PDAs), and wireless networking. Other
examples of wireless technology include GPS units, Garage door openers or garage doors, wireless
Destination
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computer mice, keyboards and Headset (audio), headphones, radio receivers, satellite television,
broadcast television and cordless telephones
There are three common types of transmission channels:
i. Wireless channels
ii. Guided electromagnetic waves channels
iii. Optical channels
The wireless channel can be the atmosphere. Due to its open nature, various noise sources are added to
the channel (Du and Swamy, 2009). Some error causing effects include:
Multipath propagation of signals
Interference from other communication devices.
Propagation path loss.
1.2 MOTIVATION
Today, wireless communication has become an integral part of everyone’s life. Communication in
adverse channels could have distortions such as dynamic noise, jamming, multi access interference,
severe fading, and dropped calls, thus prove unreliable. Wireless communication applications require
error correction schemes in order to maintain high quality of service, reliable transmission, improve
safety and provide better performance. As communication revolution evolves, there is an increasing
number of communications thriving, although with a growing shortage of bandwidth and the possibility
of errors corrupting transmission systems, there is a need to improve communication systems with
regards to protecting these systems from corruption of errors, while simultaneously enhancing the
efficiency of bandwidth use as well as providing highly reliable and error free systems which should not
be taken for granted given the nature of wireless communication channels. Error correction coding
makes wireless communications more robust in the presence of noise. The noise source is the main
focus in implementing error correcting codes.
1.3 STATEMENT OF PROBLEM
Various researches have been carried out with a view to securing and optimizing the usage of wireless
communication systems. With bandwidth requirements in communication systems, the system capacity
is depending on the level of interference that can be tolerated, and it is inversely proportional to the
signal to noise ratio (SNR) (Qian, 1999). In other words, the system capacity increases as SNR decreases.
In order to reduce SNR, error correction codes need to be integrated into the system. Error correction
codes decrease SNR by introducing the coding gain for the communication link. The coding gain
measures the amount of additional SNR required to provide the same BER performance for an uncoded
message signal (Qian, 1999).
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In 1948, Shannon proved that for a band limited Additive White Gaussian Noise (AWGN) channel, with
bandwidth B, there exist families of coding schemes that can achieve arbitrarily small probability of error
at the receiving end at a communication rate less than the capacity of the channel, which can be
described as follows:
(1.1)
Where C represents the capacity of the channel, S and N are the average signal power and noise power
respectively. The implication of equation 1.1 is that if information rate can be dropped below the
capacity of transmission channel, with proper error protection means, such as error correction codes,
error free transmission is possible. In this research, error correction is achieved using convolution codes.
1.4 SIGNIFICANCE OF RESEARCH
One of the goals of wireless communication systems is to deliver information or data efficiently and
reliably comparable to wired systems, at reasonable costs and convenience to as many users as possible.
A system with good performance should be able to deliver clear, uncorrupted data with very little
latency and minimal power consumption. In digital systems, the ability to achieve uncorrupted data
transmission is directly proportional to a system’s probability of bit error, which is in turn inversely
proportional to the power of data transmission. One of the major drives in wireless communication is
the effort to increase power efficiency, thus delivering reliable links at lower power levels. Many
practices have been developed to assist in the achievement of higher power efficiency, one of which is
the implementation of error-correction codes.
This practice involves the transmission of extra bits for redundancy in order to reduce the probability of
bit error. As expected, the transmission of extra bits requires the use of additional spectrum, which
reduces the available bandwidth for transmitting information bits, thereby resulting in a drop in
bandwidth efficiency. This illustrates a very important dilemma in wireless communication systems: the
tradeoff between power efficiency and bandwidth efficiency. Cost, convenience and mobility issues also
need to be considered in order to provide the best wireless communication systems possible.
Ultimately, each wireless communication needs to make the best tradeoff possible between all these
requirements in order to remain relevant in today’s communication environment (Jemibewon, 2000).
The cost of using error correction coding to protect the information is a reduction in data rate or an
expansion in bandwidth.
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1.5 OBJECTIVES OF THE STUDY
The main objectives chosen for this thesis are highlighted as follows:
Understand the concept of error correction in wireless communication systems.
Implementation of error correction codes in a noisy channel using convolution codes to
compensate transmission impairment in order to increase quality of transmission.
Creation of the experimental simulation model of a communication system in
MATLAB®2008/Simulink to oversee the process of error correction implementation.
Investigate the performance of the chosen codes (convolution codes) with different code rates.
1.6 THESIS OUTLINE
There are five chapters contained in this project: Chapter one is the general introduction to the
research. Chapter two entails literature reviews of related researches on error correction codes, an
overview of a wireless communication system emphasizing the important types of error correction
codes. Chapter three describes the methodology for the error correction coding in this research which is
achieved using convolution codes. Chapter four consists of the simulation results obtained in
investigating the performance of convolution codes (for two code rates), analysis and comparison of
coded and uncoded systems. Chapter five contains the summary, conclusions and suggestions for
further work.
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