report on chaotic communication

CHAOTIC COMMUNICATION

KNS Institute of Technology (affiliated to vtu , approved by AICTE)

Hegdenagar , Thirumenhalli Bangalore-560064

CERTIFICATE

Academic session : Feb 2008 – Feb 2009

This is to certify that the seminar title “CHAOTIC COMMUNICATION ,THEIR APPLICATION AND THEIR ADVANTAGES OVER TRADITIONAL METHOD” as a part of VIII semester Electronics and Communication of Vishveshwaraiah Technological University ,has been successfully done by :

Mr. RUDRAPPA J SHETTI 1KN05EC084

Date:

Signature of Staff Incharge Signature of head of the

Dept of E&C DEPARTMENT OF E&C 1 KNSIT,BANGALORE


A Seminar Report on

CHAOTIC COMMUNICATION , THEIR APPLICTION AND ADVANTAGES OVER TRADITIONAL METHOD OF

COMMUNICATION

Submitted in the partial fulfillment for the award degree of Bachelor of Engineering in Electronics and Communication

Submitted by:

RUDRAPPA J SHETTI 1KN05EC084

VISHVESHWARAIAH TECHNOLOGICAL UNIVERSITY

KNS Institute of Technology

Department of Electronics and Communication

2008-2009

DEPARTMENT OF E&C 1 KNSIT,BANGALORE


ACKNOWLEDGEMENT

I sincerely acknowledge KNS INSTIUTE OF TECHNOLOGY for providing me with the opportunity to improve my knowledge and presentation skills by giving this seminar.

I thank our Principal , Dr . S . K . Narayana ,for providing us the necessary infrastructure.

I thank our Head of Department of E&C, Prof Nanda Kumar , for his support and motivation .

I thank all the teaching and non teaching staff members of the EC department for providing the necessary help and co-operation.

Last but not the least I would like to thank all my friends for their constant support and valuable suggestion without which this would not have been the success .



SL NO. CONTENTS PAGE NO.

1 INTRODUCTION 2

2 DEFINATION OF CHAOS 4

3 CHAOTIC SYSTEM 5

4 CHAOS CONTROL 6

5CHAOTIC SIGNAL

7

6CHAOTIC SHIFT KEYING OFFER SECURE COMMUNICATION 8

7 ATTRACTOR

12



8 HISTROY OF CHAOTIC COMMUNICATION

SYSTEM 14

9

COMPARISION

34

10

ADVANTAGE

35

11

APPLICATION

36

12 CONCLUSION

37

13

BIBLIOGRAPHY

38



Abstract

The discovery of randomness in apparently predictable physical systems

have evolved into a new science, the science of chaos. Chaotic systems are unstable

and aperiodic, making them naturally harder to identify and to predict.

Recently, many researchers have been looking at ways to utilize the

characteristics of chaos in communication systems and have actually achieved quite

remarkable results. This field of communication is called Chaotic Communication .

Chaotic communication signals are spread spectrum signals, which utilize

large bandwidth and have low power spectrum density. In traditional communication

systems , the analogue sample functions sent through the channel are weight sums of

sinusoid waveforms and are linear. However, in chaotic communication systems, the

samples are segments of chaotic waveforms and are nonlinear.

This nonlinear, unstable and aperiodic characteristic of chaotic

communication has numerous features that make it attractive for communication use. It

has wideband characteristic, it is resistant against multipath fading and it offers a

cheaper solution to traditional spread spectrum systems. In chaotic communications,

the digital information to be transmitted is placed directly onto a wide-band chaotic

signal .

In this paper the concept of chaotic communication is explained together with

its applications and advantages over traditional communication methods. The

majority of the research carried out so far proves that chaotic communication system

has quite a number of advantages over traditional communication system.



1.INTRODUCTION

In communication, maintaining an ordered discipline has always been a

constraint. In order to communicate effectively and efficiently, accurate information has

to be sent or received in the correct manner. With computer processing power

increasing in the last few decades, scientists have been able to perform complicated

calculations in a relatively short period of time to facilitate this.

This in turn has given rise to scientific interest in the irregular phenomena

around us such as random changes in the weather, the spread of epidemics and the

propagation of impulses along nerves. These irregular phenomena are related to the

branch of mathematics known as chaotic dynamical systems, which deals with systems

having a kind of order without periodicity or nonlinear systems in general.

In linear systems, the variables involved appear only to the power of one.

These variables are simple and directly related. In nonlinear systems, the variables

involved are of powers other than one or even fractional. Such systems are harder to

analyze. The chaotic phenomena having no inherent order would

appear to have little to do with modern communication where sequence of zeros and

ones are sent or received accurately and reliably.

One would ask as to why then bother with chaotic communication when the

conventional communication system is managing perfectly? The answer is, in recent

experiments, digital messages were successfully sent at gigabit per second (Gbps)

speeds over 115 km of commercial optical fibre system using chaotic communication

with a Bit Error Rate (BER) of one in ten million. The BER was said to be limited by the

equipment rather than the technique itself [1].



In chaotic communication, the nonlinear characteristic of communication

devices are utilized instead of being avoided, this eliminates the complicated measures

to maintain linearity. As a result, chaotic communication systems can function over a

larger dynamical range, with fewer complex components and operate at higher power

levels than traditional communication systems.

2.The definition of chaos

There is no universally agreed definition of chaos. However, most people would accept

the following working definition:

Chaos is aperiodic time-asymptotic behaviour in a deterministic system which exhibits

sensitive dependence on initial conditions.

This definition contains three main elements:

1. Aperiodic time-asymptotic behaviour--this implies the existence of phase-space

trajectories which do not settle down to fixed points or periodic orbits. For practical

reasons, we insist that these trajectories are not too rare. We also require the

trajectories to be bounded: i.e., they should not go off to infinity.

2. Deterministic--this implies that the equations of motion of the system possess no

random inputs. In other words, the irregular behaviour of the system arises from

non-linear dynamics and not from noisy driving forces.

3. Sensitive dependence on initial conditions--this implies that nearby trajectories in

phase-space separate exponentially fast in time: i.e., the system has a positive

Liapunov exponent.



3.CHAOTIC SYSTEMS

All systems can be basically divided into three types:

Deterministic systems

These are systems for which for a given set of conditions the result can be predicted

and the output does not vary much with change in initial conditions

Stochastic systems

These systems, which are not as reliable as deterministic systems.

Their output can be predicted only for a certain range of values

Chaotic systems

Chaotic systems are the most unpredictable of the three systems.

Moreover they are very sensitive to initial conditions and a small

change in initial conditions can bring about a great change in its output



4.CHAOS CONTROL

Chaos control refers to the situation where chaotic dynamics is

weakened or eliminated by appropriate controls; while anti-control of chaos means that

chaos is created, maintained, or enhanced when it is healthy and useful. Both control

and anti-control of chaos can be accomplished via some conventional and

nonconventional methods such as microscopic parameter perturbation, bifurcation

monitoring, entropy reduction, state pinning, phase delay, and various feedback and

adaptive controls.

It has been shown that the sensitivity of chaotic systems to small

perturbations can be used to direct system trajectories to a desired target quickly with

very low and ideally minimum control energy

Chaos may be used to enhance the artificial intelligence of neural

networks, as well as increase coding- decoding efficiency in signal and image

communications.



5.CHAOTIC SIGNALS

• Chaotic signals has broadband spectrum , hence the presence of information

does not necessarily change the properties of the signal .

• Power output remains constant regardless of information content.

• It is resistant against multipath fading and offers cheaper solution to traditional

spread spectrum systems.

• Chaotic signals are aperiodic therefore limited predictability.

• Chaotic signals are complex in structure and impossible to predict over long

time.

• chaotic signals appear noise like

• Hence chaotic signal can be used for providing security at physical level.



6.Chaotic-shift keying offers secure communication

OPTICAL ENCRYPTION

Researchers have been making progress toward practical

optical encryption systems that exploit laser dynamics. In two recent papers,

researchers in France and Japan have shown how feedback-loop-based systems

can be best used, and have introduced a new kind of modulation scheme. The

separate results demonstrate both the security and ease of decoding of one

class of the emerging chaotic-shift keying (CSK) systems, and the applicability of

the other to a wide range of systems.

Chaotic-shift keying uses fluctuations in wavelength to encode

and hide a communications signal. In an optoelectronic implementation, a laser is

configured so that its output fluctuates chaotically—that is, in a deterministic way

that nevertheless looks random. To change from one bit value to another (1 to 0

or vice versa) the chaotic mechanism is altered slightly. Because the output is

still chaotic, an eavesdropper should not see any change in the transmission.

However, the receiver detects that the chaos is sometimes synchronized,

sometimes not, allowing the signal to be extracted.



FIGURE 1. In a chaotic-shift keying scheme, the output of a tunable distributed Bragg reflector laser is fed back

via a nonlinear spectral filter and time delay, causing a chaotic shift in wavelength. The chaos is modulated by the input

signal, which varies the delay between time intervals T0 (511.5 µs) and T1 (543.2 µs). This modulation is then picked up by

a receiver matched to T0, and the error signal (where the signal and receiver are unsynchronized) shows the location of

the nonmatching bits(ones)

In collaboration between researchers at Georgia Tech Lorraine

(Metz, France) and the Laboratoire d'Optique at the Université de Franche-

Compté (Besançon, France), researchers have demonstrated that this system

can achieve high-fidelity, high-security recordings. In their system, the

researchers use a feedback loop with a nonlinear spectral filter to provide the

mechanism for chaotic emission from distributed Bragg reflector lasers (see Fig.

1).1



THREE OPTIONS

The French team wanted to quantify the advantages of changing different

parameters to shift from bit to bit. Initially they considered three options: the

mean wavelength (around which the chaos was fluctuating), the bifurcation

parameter related to the dynamics of the photodetector and laser diode, and the

time delay implemented in the feedback loop.

FIGURE 2. By representing ones and zeros as different time delays in the laser feedback circuit

(top), the data remained securely hidden in the chaotic signal (center), and yet could be recovered

without additional signal processing (bottom). (Photo courtesy of Georgia Tech Lorraine)

The least sophisticated option is known as masking: essentially a small

wavelength modulation signal is hidden in a large chaotic one. This makes it both

difficult to decode and somewhat insecure, since the modulation could be

detected by an eavesdropper. Tweaking the bifurcation parameter was also

inadequate for the encryption application: for more than 50% of bits to be



correctly recognized, the mismatch between the bifurcation parameter had to be

less than 0.03. For better than 98% masking (high security), the mismatch had to

be more than 0.035.

Changing the time delay in the feedback loop, however, was successful. The re-

searchers showed that the bit seq-uence was well-hidden and easily received

(see Fig. 2), and the signal could not be decrypted by looking at the signal

spectrum or through autocorrelation.

ALTERNATIVE METHOD

In another project, a collaboration between engineers at Takushoku

and Keio Universities (both of Tokyo, Japan), researchers chose to use an

acousto-optic modulator (AOM) to degrade CSK synchronization for the

nonmatched states.2 This approach does not depend on the type of chaotically

emitting laser used, so it could be used with semiconductor lasers that have very

fast oscillations. For this scheme to work at high speeds, however, the transient

time for synchronization—currently 10 times the AOM frequency—will have to be

shortened.

•



7.CHAOTIC ATTRACTOR

Also known as a strange attractor, a type of

attractor (i.e., an attracting set of states) in a

complex dynamical system's phase space

that shows sensitivity to initial conditions.

Because of this property, once the system is

on the attractor nearby states diverge from

each other exponentially fast. Consequently,

small amounts of noise are amplified. Once

sufficiently amplified the noise determines

the system's large-scale behavior and the

system is then unpredictable. Chaotic

attractors themselves are markedly

patterned, often having elegant, fixed

geometric structures, despite the fact that

the trajectories moving within them appear unpredictable. The chaotic attractor's

geometric shape is the order underlying the apparent chaos. It functions in much the

same way as someone kneading dough. The local separation of trajectories

corresponds to stretching the dough and the global attraction property corresponds to

folding the stretched dough back onto itself. One result of the stretch-and-fold aspect of

chaotic attractors is that they are fractals; that is, some cross-section of them reveals

similar structure on all scales.


The Lorentz attractor: the best-known chaotic attractor


TYPES OF ATTRACTOR

1. FIXED POINT ATTRACTOR

An attractor that is represented by a

particular point in phase space ,sometime called an equilibrium point .As a point

it corresponds to a very limited range of possible behaviors of the system.

2. LIMITED CYCLE ATTRACTOR

A LIMIT CYCLE IS A PERIODIC ORBIT OF THE SYSTEM IS ISOLATED .



8.History of chaotic secure communication

Chaos is a very universal and robust phenomenon in many nonlinear systems.

Although the area mathematician Pincar´e had noted that some mechanical

systems could behave chaotically [21], chaos did not attract wide attention until

Lorenz published his paper in 1963[22].

In engineering community, chaos had been mixed with

noise for a long time. In 1980’s, the electrical engineers first time “officially”

announced the existence of chaos in electrical systems. Since the noise-like

behaviors of chaotic electronic circuits, electrical engineers felt uncomfortable to

deal with them. It was physicists first showed in 1990 that chaos could be

controlled [2].

Then the synchronization between two identical chaotic systems was reported

in1990 [23]. In 1992, the electrical engineering community realized that chaos

could used in secure communication systems [24, 25, 26 ] because chaos is

extremely sensitive to initial conditions and parameters. The concept of chaotic

hardware key for secure communication systems was then gradually realized by

engineers and scientists .Since the great potential of applying chaos to secure

communication systems, many groups over the world involved in the researches

in this field. So far, chaotic communication systems have been updated to the

fourth generation. In this paper, theory and structure of the fourth generation is

presented. It is useful to provide the reader who is not involved in chaotic secure



First generation

The first generation was developed in 1993 known as additive chaos masking [25]

shown in Fig. 1(a) and chaotic shift keying [26] shown in Fig. 1(b). The additive chaos

masking scheme shown in Fig.1(a) consists of two identical chaotic systems in both the

transmitter and the receiver. The chaotic mask denoted by c(t) is one of the state

variables of the chaotic system2 in the transmitter. The message signal m(t), which is

typically 20 dB to 30dB weaker than c(t) is added into the chaotic mask signal and gives

the transmitted signal s(t). Since the chaotic signal c(t) is very complex and m(t) is much

smaller than c(t), one may hope that the message signal m(t) can not be separated from

s(t) without knowing the exact c(t).To give the reader a hands-on experience on chaotic

secure communication systems, an example of additive chaotic masking scheme is

given as follow. From Fig. 1(a) we can see that a chaotic synchronization block is

needed in the receiver. Chaotic synchronization is a generalization of “carrier

synchronization” in the normal communication systems but it is very different from the

latter. We use Chua’s oscillators to demonstrate the

chaotic synchronization. A Chua’s Oscillator is shown in Fig. 2(a)



This scheme was proved that it could not be used under

practical conditions because of the following drawbacks. Since the message signal is

typically 20dB to 30dB weaker than the “chaotic mask”, this method is very sensitive to

channel noise and parameter mismatch between the chaotic systems in the transmitter

and the receiver. Furthermore, this scheme has a very low degree of security[8].

Chaotic shift keying shown in Fig. 1(b) also known as chaotic

switching was designed to transmit digital message signal. In this scheme, the message

signal, which is a digital signal, is used to switch the transmitted signal between two

statistically similar chaotic attractors, which are respectively used to encode bit 0 and bit

1 of the message signal. These two attractors are generated by two chaotic systems

with the same structure and different parameters. At the receiver end, the received

signal is used to drive achaotic system, which is identical to any of the two chaotic

filtering and then thresholding the synchronization error signal e(t), which is depicted in

Fig. 1(b).



This scheme is very robust to noise and parameter mismatch. However, it has a low

degree of security[7] if the chaotic attractors are too far away in the bifurcation space.

However, since this is the first scheme of chaotic digital communication systems, there

still exist many possibilities of improving it.



Second generation :

The second generation was proposed during 1993 to 1995

known as chaotic modulation. This generation used two different ways to modulate

message signals into chaotic carriers. The first method called chaotic parameter

modulation [27] shown in Fig. 7(a) used message signals to change parameters of the

chaotic transmitter. The second method called chaotic non-autonomous modulation [28]

shown in Fig. 7(b) used the message signal to change the phase space of the chaotic

transmitter.



In Fig. 7(a) the message signal m(t) is used to modulate some parameters of the

chaotic system in the transmitter such that its trajectories keep changing in different

chaotic attractors. Since the bifurcation space of a chaotic system is very complex, it is

very difficult to figure out the way of the changes of the parameters even through the

intruder knows some partial knowledge of the structure of the chaotic system in the

transmitter. At the receiver end an adaptive controller is used to adaptively tune the

parameters of the chaotic system such that the synchronization error approach zero.

By doing this, the output of the adaptive controller can recover the message signal. The

simulation results are shown in Fig. 8. In this simulation, three message signals are

used to tune three different parameters of the chaotic system in the transmitter. Since

the chaotic system keeps changing its attractors, the waveform of the transmitted signal

as shown in Fig. 8(a) is much more complex than a normal chaotic signal. In Figs.8(b)

to (d) we show the three original message signals and the three recovered message

signals. Observe that after a transient process of synchronization, the message signals

are recovered with some cross talks and small delays.

Instead of changing the parameters of the chaotic transmitter, the

chaotic

non-autonomous modulation shown in Fig. 7(b) used the message signal to perturb

chaotic attractor directly in the phase space. Unlike in chaotic parameter modulation

where the transmitter is switched among different trajectories in different chaotic

attractors, the transmitter in chaotic non autonomous modulation is switched among

different trajectories of the same chaotic attractor. Theoretically, chaotic non-

autonomous modulation is an error free scheme. The second generation improved the

degree of security to some degree but was still found unsatisfactory.



Third generation:

The third generation shown in Fig. 9 was proposed in 1997[9] for the

purpose of improving the degree of security to a much higher level than the first two

generations. We call this generation as chaotic cryptosystem. In this generation, the

combination of the classical cryptographic technique and chaotic synchronization is

used to enhance the degree of security. So far, this generation has the highest security

in all the chaotic secure communication systems had been proposed and has not yet

been broken. In the chaotic cryptosystem the plain text signal p(t) is encrypted by a

encryption rule with a key signal, k(t), which is generated by the chaotic system in the

transmitter. The scrambled signal is used further to drive the chaotic system such that

the chaotic dynamics is changed chaotic system in the transmitter is transmitted to

through public channel which can be accessed by the intruder. Since the intruder can

not get access to the chaotic hardware key, it is very difficult to find p(t) out from s(t). At

the receiver, the received signal r(t) = s(t)+n(t), where n(t) is the channel noise, is used

to synchronize both of the chaotic systems in transmitter and the receiver. After the



chaotic synchronization had been achieved, the signal k(t) and y(t) can be recovered at

the receiver with some noises as denoted by ˜k(t) and ˜y(t). By feeding ˜k(t) and ˜y(t)

into the decryption rule at the receiver, the plain text signal can be recovered with some

noises as ˜p(t). The simulation result is shown in Fig. 10. Figure 10(a) shows the

transmitted signal s(t), from which one can not observe the embedded plain signal.

Figure 10(b) shows the recovered and decrypted result at the receiver. Observe that

after the transient process of synchronization, the plain text signal is recovered. To

show the high security of this scheme, the unmasking method provided in [18] is used

to decode the plain text signal. Figure 10(c) shows the unmasked signal ˜y(t) by the

intruder, from which it is impossible to retrieve the plain text signal as shown in Fig.

10(d).

Fourth generation:



Since the publication of several chaotic cryptanalysis results in low

dimensional chaos-based secure communication systems[7, 8, 16, 18], there were

concerns that such communication schemes may not be secure enough. To overcome

this objection, one approach is to exploit hyperchaos-based7 secure communication

systems, but such systems may introduce more difficulties to synchronization. On the

other hand, we can enhance the security of low-dimensional chaos based secure

communication schemes by combining conventional cryptographic schemes with a

chaotic system[9]. To overcome the low security objections against low-dimensional

continuous chaos-based schemes, we may use the following two methods. The first

method is to make the transmitted signal more complex. The second method is to

reduce the redundancy in the transmitted signal. In [9] we have

presented a method to combine a conventional cryptographic scheme with low-

dimensional chaos to obtain a very complex transmitted

signal. The impulsive synchronization presented in this paper offers a very promising

approach of reducing the redundancy in transmitted signals.

A simple system in baseband .

In this section, we combine the results in [9] and impulsive

synchronization to give a new chaotic secure communication scheme. The

block diagram of this scheme is shown in Fig. 19. From Fig. 19 we can see

that this chaotic secure communication system consists of a transmitter and

a receiver. In both the transmitter and the receiver, there exist two identical

chaotic systems. Also, two identical conventional cryptographic schemes are

embedded in both the transmitter and the receiver. Let us now consider the

details of each block in Fig. 19. The transmitted signal consists of a sequence

of time frames. Every frame has a length of T seconds and consists of two

regions.



In Fig. 20 we show the concept of a time frame and its components. The

first region of the time frame is a synchronization region consisting of synchronization

impulses. The synchronization impulses are used to impulsively synchronize the chaotic

systems in both transmitter and receiver. The second region is the scrambled signal

region where the scrambled signal is contained. To ensure synchronization, we have T

< ¢max. Within every time frame, the synchronization region has a length of Q and the

remaining time interval T ¡ Q is the scrambled signal region. The composition block in

Fig. 19 is used to combine the synchronization impulses and the scrambled signal into

the time frame structure shown in Fig. 20.

The simplest combination method is to substitute the beginning Q

seconds of every time frame with synchronization impulses. Since Q is usually very

small compared with T, the processing time for packing a message signal is negligible.

The decomposition block is used to separate the synchronization region and the

scrambled signal region within each frame at the receiver end. Then the separated

synchronization impulses are used to make the chaotic system in the receiver to

synchronize with that in the transmitter. The stability of this impulsive synchronization is

guaranteed by our results in Section 4. In the transmitter and the receiver, we use the

same cryptographic scheme block for purposes of bi-directional communication. In a

bi directional communication scheme, every cellular phone should function both as a

receiver and a transmitter. Here, the key signal is generated by the chaotic system .The



cryptographic scheme is as follows [9]:

Fig: Time frame



9.Conventional Sinusoidal-based Communication vs. Chaos-based Communication

Conventional Chaotic

History: over 100 years old; less than 10 years old;

matured technology Emerging technology

Industrial Heart of world wide None existing

base inform. Tech.

Transmission Transmit either Transmit at wide BW

bandwidth at information BW

or at wide BW

(Spread Spectrum)

Relation between Distinct separation Many CC sys. schemes

theory & Tech. between info. the./ are described

comm. sys./comm. by chaotic circuits

circuits-hardware

implementation

Modulation non-BW expansion BW expansion Formats: Anti-podal signals; Chaotic masking;

BPSK; BFSK Parametric modulation

Dynamic feedback

Synchronization

Theory of Sync. For Chaotic sync. is

AFC and PLL are well still an active research

Conventional Chaotic



developed; implementational area; loss from

theory is only loss of fraction of performance due

a dB; No sync. Needed for implementation is

BSK more significant

Encryption: No yes

Bit Prob. Error: Exist analytic error No known analytic

Expr. error Expr.

Complexity: simple complex



10.Advantages over Traditional Methods

1. At high speed it is easier to generate strong , high power chaotic signals than periodic

signals.

2. Chaotic signals are not sensitive to initial conditions and have

noise like time series

3. Chaotic transmission has less risks of interception and are hard to detect by

eavesdropper.

4. In chaotic communication, then on linear characteristic of communication devices

are utilized instead of being avoided, this eliminates the complicated measures to

maintain linearity.

5. Chaotic communication systems can function over a larger dynamical range, with

fewer complex components and operate at higher power levels than traditional

communication systems .

6. The optimal asynchronous CDMA codes using chaotic spread-spectrum sequences

can support 15% more users than the standard GOLD codes for the same bit error rate

(BER) performance.

7. It has auto cross correlation properties, low multipath interference and self-

synchronization property.

8. Power output remains constant regardless of the information content.

9. It is resistant against multi-path fading and offers cheaper solution to traditional

spread spectrum systems.

10. Chaotic signal are aperiodic therefore limited predictability.



11.Application of chaos in digital communication



Applications of chaotic communication

Used in secure communication.

Used in Ultra Wide Band radio.

Used in radar and sonar.

Used in oscillator

Used in modulation technique

Used in spread spectrum

Used for secure communication



12.CONCLUSION

A very brief overview on Chaotic Communication has been

described, explaining the system setup of synchronised chaotic

communication and direct chaotic communication with

comparison to traditional communication system setup. A few of

the main chaotic modulating schemes have been described,

however, it was not possible to explain some of them in depth

due to space limitations. The majority of the research carried out

so far proves that chaotic communication system has quite a

number of advantages over traditional communication

Every technology has its own advantages and disadvantages.We

also had an over view of history of chaotic secure

communications. We studied about attractors, chaotic systems

and signal. Comparison of conventional over chaotic

communication and their applications. Therefore, chaotic

communication has to be used sensibly , it should lead to human

integrity and benefit to the mankind.



BIBLIOGRAPHY

[1] J. Mullins, “Chaotic Communication”,

(http://www.spectrum.ieee.org/jan06/2574 [Accessed

29/11/2007].

[2] G. Kolumban, M.P. Kennedy, and L. O. Chua, “The role of

synchronization in digital communication using chaos – Part II:

Chaotic Modulation and Chaotic Synchronization”, IEEE Trans.

Circuits Syst. I

[3] G. Kolumban, M.P. Kennedy, and L. O. Chua, “The role of

synchronization in digital communication using chaos – Part I:

Fundamentals of digital communication”, IEEE Trans. Circuits

Syst. I

[4] Digital communication using chaos and Non-linear dynamic

book

E.Larson,Liu-ming,Liu lew.s

Website referred

www.dbebooks.comDEPARTMENT OF E&C 1 KNSIT,BANGALORE

http://www.dbebooks.com/


www.google.com

www.tech-faq.com http//en.wikipedia.org/wiki/


http://www.tech-faq.com/

http://www.google.com/

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