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Available online at www.ijarbest.com
International Journal of Advanced Research in Biology, Ecology, Science and Technology (IJARBEST)
Vol. 1, Issue 1, April 2015
All Rights Reserved © 2015 IJARBEST 1
 Chaotic Secure Communication Using Iterated
Filtering Method
P. Karthik 1
, D. Gokul Prashanth 2
, T. Gokul 3
Assistant Professor, Department of Electronics and Communication Engineering,
SNS College of Engineering, Coimbatore, India 1
Under Graduate Scholar, Department of Electronics and Communication Engineering,
Under Graduate Scholar, Department of Electronics and Communication Engineering,
Abstract—The communication process is one of the fast
developing field which demands security as well as performance.
For achieving high security, many chaos synchronization
schemes have been proposed which are compromising the
performance of the system. Also the chaos synchronization
controller is not robust and adaptable to different working
conditions. Thus, achieving a high security for the information
at lowest possible performance degradation is a major challenge.
This proposal aims to overcome this challenge by introducing
a new approach that employs the use of Iterated Filtering
Algorithm (IFA). The real time speech signal (i.e. a recorded
audio) is mixed with the chaotic signal (generated by
Gingerbreadman Map) at the transmitter side and then the
audio signal is separated by the Iterated Filtering Algorithm
(IFA) at the receiver side.
It offers an efficient method to estimate the median without
time consuming data sorting techniques. Thus, it is used here to
recover the speech signal from the mixed signal.
Index Terms—Iterated Filtering Algorithm (IFA),
Gingerbreadman Map, Chaotic Signal.
I. INTRODUCTION
The word “chaos” means “a state of disorder”. Where the
present determines the future, but the approximate present
does not approximately determine the future.
Chaos theory is concerned with the deterministic systems
whose behavior can be predicted. Chaotic systems are
predictable for a while and then appear to become random.
The amount of time for which the behavior of a chaotic system
can be effectively predicted depends on three things: How
much uncertainty we are willing to tolerate in the forecast;
how accurately we are able to measure its current state; and a
time scale depending on the dynamics of the system , called
the Lyapunov time. In chaotic systems the uncertainty in a
forecast increases exponentially with elapsed time. Hence
doubling the forecast time more than squares the proportional
uncertainty in the forecast. This means that in practice a
meaningful prediction cannot be made over an interval of
more than two or three times the Lyapunov time. When
meaningful predictions cannot be made, the system appears to
be random. Thus, it is widely used in the communication
process for hiding the information.
Iterated Filtering Algorithms (IFA) are a tool for maximum
likelihood inference for partially observed dynamical
systems. Stochastic perturbations of the unknown parameters
are used to explore the parameter space. Applying sequential
Monte Carlo (the particle filter) to this extended model result
in the selection of the parameter values that are more
consistent with the data. Iterated filtering methods have so far
been used most extensively to study the infectious disease
transmission dynamics.
This IFA process is employed here to separate the mixed
audio and chaotic signal.
II. IMPLEMENTATION TOOL
MATLAB (Matrix Laboratory) is a numerical computing
environment and fourth-generation programming language
developed by Math Works. MATLAB allows matrix
manipulations, plotting of functions and knowledge,
implementation of algorithms, creation of user edges, and
interfacing with programs written in alternative languages,
together with C, C++, Java, and FORTRAN. MATLAB is a
simulation tool that is helpful in finding out the dynamic
nature of the communication networks.
III. EXISTING SYSTEM
A. Emperical Mode Decomposition (EMD)
The starting point of the Empirical Mode Decomposition
(EMD) is to consider oscillations in signals at a very local
level. In fact, if we look at the evolution of a signal x(t)
between two consecutive extrema (say, two minima occurring
at times t− and t+), we can heuristically define a (local)

high-frequency part {d(t),t− ≤ t ≤ t+}, or local detail, which
corresponds to the oscillation terminating at the two minima
and passing through the maximum which necessarily exists in
between them. For the picture to be complete, one still has to
identify the corresponding (local) low-frequency part m(t), or
local trend, so that we have x(t) = m(t) + d(t) for t− ≤ t ≤ t+.
Assuming that this is done in some proper way for all the
oscillations composing the entire signal, the procedure can
then be applied on the residual consisting of all local trends,
and constitutive components of a signal can therefore be
iteratively extracted.
Given a signal x(t), the effective algorithm of EMD can be
summarized as follows:
1. Identify all extrema of x(t).
2. interpolate between minima (resp. maxima), ending
up with some envelope emin(t) (resp. emax(t))
3. Compute the mean,
m(t) = (emin(t)+emax(t))/2
4. Extract the detail, d(t) = x(t) − m(t)
5. Iterate on the residual m(t).
In practice, the above procedure has to be refined by a
sifting process which amounts to first iterating steps 1 to 4
upon the detail signal d(t), until this latter can be considered as
zero-mean according to some stopping criterion. Once this is
achieved, the detail is referred to as an Intrinsic Mode
Function (IMF), the corresponding residual is computed and
step 5 applies. By construction, the number of extrema is
decreased when going from one residual to the next, and the
whole decomposition is guaranteed to be completed with a
finite number of modes.
IV. PROPOSED SYSTEM
The real time speech signal (i.e. a recorded audio) is mixed
with the chaotic signal (generated by Gingerbreadman Map)
with added noise at the transmitter side. The noise level can be
set according to the requirement. Then, the audio signal is
separated by the Iterated Filtering Algorithm at the receiver
side. The Fig.1 depicts the above.
Fig.1 – Block Diagram
Here, the real time audio signal can be a recorded voice
(speech) from a recording device viz. Mobile phones, etc.
This audio file is given as input to the MATLAB. When it is
displayed in the graphical form, it looks like the following
figure.
Fig.2 – Input Signal (Audio)
Now, The chaotic signal is required to add it with the audio.
It is generated using Gingerbreadman Map.
V. GINGERBREADMAN MAP CHAOTIC SYSTEM
In dynamical systems theory, the Gingerbreadman map is a
chaotic 2D map. It is given by the transformation (1) and (2):
(1)
(2)
This describes the sensitivity of the initial conditions in a
chaotic system. A consequence of sensitivity to initial
conditions is that if we start with only a finite amount of
information about the system, then beyond a certain time, the
system will no longer be predictable.
Fig.3 – Gingerbreadman Map
As the Gingerbreadman Map has been already available, it
is easily predictable. Thus, in order to make it more
complicate, the initial values are changed and an additional
noise of known level is added to it. Now, the Gingerbreadman
Map looks like the following Fig.4.
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
4
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Fig.4 – Gingerbreadman Map with Added Noise
VI. MIXING OF AUDIO SIGNAL WITH THE CHAOTIC SIGNAL
The input audio signal is mixed with the above generated
chaotic signal. This will hide the original signal. The plot of
the mixed signal is shown by Fig.5.
Fig.5 – Mixed Signal
Here, the information is hidden to the outside world. Thus,
this signal is transmitted from the sender side which can be
wired or wireless transmission.
VII. ITERATED FILTERING ALGORITHM – RECEIVER
The transmitted signal is received at the receiver side. In
order to recover the original message signal from the received
signal, the Iterated Filtering Algorithm is employed. Here,
Weighted Iterative Truncated Mean Filter requires the mean
and weighted mean filter values. Thus, these are first
calculated.
In general, a filter output is the result of an operation on a
group of inputs within a filter window. Suppose, the filter
window contains n inputs residing in a data set xo = {xi}, 1 ≤
i ≤ n. The mean and median filters, respectively, produce
outputs µo=mean(xo) and
In general, the outputs of mean filter µo and median filter
are different. Changing the stopping criteria of the iteration,
the filter can produce an output closer to the arithmetic mean.
B. Outline of the Iterative Truncated Mean Filter (ITM)
Starting from x = xo, the ITM algorithm consists of three
steps:
1. Compute the arithmetic mean, i.e.,
µ = mean(x)
2. Compute dynamic threshold τ and truncate input data
set x = {xi} by:
xi = , 1 ≤ i ≤ n
3. Return to step 1. if stopping criterion S is violated.
Otherwise, terminate the iteration.
The weighted mean is the maximum likelihood (ML)
estimate of location for data sets with Gaussian distribution.
Assume a filter window contains n independent Gaussian
distributed samples as xo = {x1, x2,.....xn} with unknown
constant mean µo. The variance of the ith sample is . The
ML estimate of location µo is to find the value of µ, which
maximizes the likelihood function. Now, the truncation
procedure of the ITM filter is caried out.
C. Truncation procedure of the ITM Filter
Input: xo = x ; Output: Truncated x;
1. Compute the sample mean:
µ = mean(x);
2. Compute the dynamic threshold:
τ = mean(x - µ);
3. bl = µ - τ, bu = µ + τ, and truncate x by:
xi =
4. Return to step 1, if stopping criterion S is violated.
The weighted Iterative Truncated Mean filter (WITM) is
proposed based on the following theorems 1 and 2.
Theorem 1: For any finite data set x = {x1, x2,......xn} and
weight set w = {w1, w2, ....wn} with all weights being
non-negative rational numbers, the difference between the
weighted mean µw and weighted median w is never great
than the weighted mean absolute deviation τw. The
corresponding formula is:
Theorem 2: For any finite data set x and weight set w, there
exists at least one sample whose distance from the weighted
mean µw is greater than the weighted mean absolute deviation
τw if the weighted mean µw deviates from the weighted median
w, i.e.,
, that |xi - µw| τw, if µw = w
-15 -10 -5 0 5 10 15
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Chaotic Signal withAdded Noise
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D. Truncation procedure of the WITM Filter
Input: w,xo x ; Output: Truncated x;
1. Compute the weighted mean:
;
2. Compute the weighted dynamic threshold:
;
3. bl = µw – τw, bu = µw + τw, and truncate x by:
xi =
4. Return to step 1. if stopping criterion S is violated.
VIII. SIMULATION RESULTS
The mixed signal is passed through the mean and weighted
mean filters in order to obtain the mean and weighted mean.
After that, these are given as input to the Weighted Iterative
Truncated Mean Filter, which recovers the audio. The mean
and weighted mean filter outputs are shown below.
Fig.6 - Mean Filter Output
Fig.7 – Weighted Mean Filter Output
Fig.8 – Weighted Iterative Truncated Mean Filter Output
Thus, the Weighted Iterative Truncated Mean Filter
(WITM) recovers the original message i.e. speech signal from
the mixed signal. The Fig.8 shows the recovered signal which
is similar to the initial input signal.
IX. CONCLUSION
In this project we have provided an alternative algorithm
for the empirical mode decomposition (EMD) using iterative
filters (IFs). This alternative approach replaces the mean of
the spline-based envelopes in the original sifting algorithm by
an adaptively chosen moving average. The use of a moving
average allows in many cases for a more rigorous
mathematical analysis of this proposed alternative EMD.
Thus, the security of the speech information can be
achieved by using this iterated filtering technique. It can be
used in the simple communication process between two ends
where we need to hide the information. The future work of
this project includes the increasing the speed of the process in
order to bring it in a real time conversation. Also, the use of
other different chaotic systems may improve the efficiency of
this process.
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Mr. P. Karthik was born on 31st
July 1982. He did
his B.E – ECE in Franxis Xavier Engineering
College, M.S. University in 2004 and M.E
(Computer and Communication Engineering) in
Hindustan College of Engineering and Technology in
the year 2010. He is currently working as Assistant
Professor in Department of Electronics and
Communication Engineering in SNS College of
Engineering. His area of specialization is
Communication and published papers in several National and International
Conferences and Journals
Mr. D. Gokul Prashanth was born on 12th
December
1992. He is currently pursuing his B.E – ECE in SNS
College of Engineering, Coimbatore. His area of
interest is Communication. He published paper in
National Conference ‘TAPSA’15’ at Sri Krishna
College of Engineering and Technology, Coimbatore.
Mr. T. Gokul was born on 21th
June 1993. He is
currently pursuing his B.E – ECE in SNS College of
Engineering, Coimbatore. His area of interest is
Communication and also includes programming. He
published paper in National Conference ‘TAPSA’15’
at Sri Krishna College of Engineering and
Technology, Coimbatore.

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