Draft IJCSIS Volume 1 May 2009.pdf

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News & Politics
International Journal of 
Computer Science 
& Information Security 
 
 
 
 
 
 
© IJCSIS PUBLICATION 
Vol. 1, No. 1, May 2009 
ISSN 1947-5500 
Editorial 
Message from Managing Editor 
 
 
Welcome to the first issue of IJCSIS (International Journal of Computer Science and 
Information Security). The primary aim of this journal  to disseminate new knowledge 
and technology for the benefit of everyone ranging from the academic and professional 
research communities to industry practitioners in a range of topics in computer science 
& engineering in general and information & communication security, mobile & 
wireless networking, and wireless communication systems. It also provides a venue for 
researchers, students and professionals to submit on-going research and developments 
in their areas of interest. 
 
40 papers were submitted to IJCSIS for the May 2009 Special Issue and the acceptance 
rate was 30%. The revision process for all papers was rigorous, including peer-
reviewing from at least two qualified reviewers. The accepted papers are of good 
quality and cover the wide range of topics, such as Computer Network, Wireless 
Security and Algorithms. 
 
It is our pleasure to introduce you these accepted papers. 
 
Available at http://sites.google.com/site/ijcsis/  
IJCSIS Vol. 1, No. 1, 31 May 2009. 
IJCSIS EDITORIAL BOARD 
 
 
Gregorio Martinez Perez 
Associate Professor - Profesor Titular de Universidad 
University of Murcia (UMU), Spain 
 
 
Dr. Sanjay Jasola  
Professor and Dean 
School of Information and Communication Technology, 
Gautam Buddha University, 
Greater NOIDA (Gautam Buddha Nagar) 
 
 
Dr Riktesh Srivastava 
Assistant Professor, Information Systems 
Skyline University College, University City of Sharjah, 
Sharjah, PO 1797, UAE 
REVIEWERS’ LIST of IJCSIS Publications 2009 
 
 
1. Dr. Lam Hong Lee, Universiti Tunku Abdul Rahman, Malaysia 
2. Assoc. Prof. N. Jaisankar, VIT University, Vellore,Tamilnadu, India 
3. Dr. Amogh Kavimandan, The Mathworks Inc., USA 
4. Dr. Ramasamy Mariappan, Vinayaka Missions University, India 
5. Dr. Neeraj Kumar, SMVD University, Katra (J&K), India 
6. Dr. Junjie Peng, Shanghai University, P. R. China 
7. Dr. Ilhem LENGLIZ, HANA Group - CRISTAL Laboratory, Tunisia 
8. Prof. Dr. Durgesh Kumar Mishra, Acropolis Institute of Technology and Research, 
Indore, MP, India 
9. Prof. Dr.C.Suresh Gnana Dhas, Anna University, India  
10. Prof. Pijush Biswas, RCC Institute of Information Technology, India 
11. Dr. A. Arul Lawrence, Royal College of Engineering & Technology, India 
12. Mr. Wongyos Keardsri, Chulalongkorn University, Bangkok, Thailand 
13. Mr. Somesh Kumar Dewangan, CSVTU Bhilai (C.G.)/ Dimat Raipur, India 
14. Mr. Hayder N. Jasem, University Putra Malaysia, Malaysia 
15. Mr. A.V.Senthil Kumar, C. M. S. College of Science and Commerce, India 
16. Mr. R. S. Karthik, C. M. S. College of Science and Commerce, India 
17. Mr. P. Vasant, University Technology Petronas, Malaysia 
18. Mr. Wong Kok Seng, Soongsil University, Seoul, South Korea 
19. Mr. Praveen Ranjan Srivastava, BITS PILANI, India 
20. Mr. Kong Sang Kelvin, The Hong Kong Polytechnic University, Hong Kong 
21. Mr. Mohd Nazri Ismail, Universiti Kuala Lumpur, Malaysia 
22. Dr. Rami J. Matarneh,  Al-isra Private University, Amman,  Jordan 
23. Dr Ojesanmi Olusegun Ayodeji, Ajayi Crowther University, Oyo, Nigeria 
24. Dr. Siddhivinayak Kulkarni, University of Ballarat, Ballarat, Victoria, Australia 
25. Dr.  Riktesh Srivastava, Skyline University, UAE  
26. Dr. Oras F. Baker, UCSI University - Kuala Lumpur, Malaysia 
27. Dr. Ahmed S. Ghiduk, Faculty of Science, Beni-Suef University, Egypt 
 and Department of Computer science, Taif University, Saudi Arabia 
28. Assist. Prof. Tirthankar Gayen,  CIT, West Bengal University of Technology, India 
29. Ms. Huei-Ru Tseng, National Chiao Tung University, Taiwan 
30. Prof. Ning Xu, Wuhan University of Technology, China 
31. Mr Mohammed Salem Binwahlan, Hadhramout University of Science and 
Technology, Yemen & Universiti Teknologi Malaysia, Malaysia. 
(IJCSIS) International Journal of Computer Science and Information Security, Vol. 1 No.1 May 2009 
 
Manuscript received , April 2009 
Manuscript revised , May 2009 
Strategies and Performances of Soft Input Decryption 
Natasa Zivic†  
natasa.zivic@uni-siegen.de 
University of Siegen,  Hoelderlinstrasse 3, Siegen, Germany 
 
Summary 
This paper analyzes performance aspects of Soft Input 
Decryption and L-values. Soft Input Decryption is a novel 
method which uses L-values (soft output) of a SISO 
channel decoder for the correction of input of Soft Input 
Decryption (SID blocks) which have been modified during 
the transmission over a noisy channel. The method is 
based on the combination of cryptography and channel 
coding improving characteristics of both of them. The 
algorithm, strategies and scenarios of Soft 
Input 
Decryption are described. 
 
The results of the tested performance of L-values show 
how many L-values are necessary for the correction of 
SID blocks. This number is higher than the number of 
wrong bits. This difference is presented. The number of L-
values is estimated for different lengths of SID blocks as 
well as for different Eb/N0 ratios.  Space characteristics of 
L-values are not analyzed, because they depend on the 
used SISO decoding algorithm. In this paper, Maximum 
A-Posteriori (MAP) algorithm is used. 
 
The time performance of Soft Input Decryption depends 
on the used cryptographic mechanism for the verification 
of the cryptographic check values (digital signatures 
(based on Elliptic Curve Cryptography), MACs (based on 
CBC-DES) and H-MACs (based on SHA-1)).  
 
The combination of the performance of L-values and time 
performance gives an estimation, if and when Soft Input 
Decryption can be performed in practice. Further 
optimizations are outlined. 
 
Key words: 
Soft Input Decryption, SISO Channel Decoding, Joint 
Channel Coding and Cryptography, Digital Signatures, 
Elliptic Curve Cryptography. 
1. Introduction 
The combination of a SISO decoder and Decryptor, which 
is analyzed in this paper, can be considered as a 
concatenation of codes: en-/decryptor has the role of an  
 
 
 
outer en-/decoder and the channel encoder/SISO channel 
decoder has the role of an inner en-/decoder has (Fig. 1). 
 
Concatenation of codes, presented as an outer and inner 
code was already devised by Forney in 1966 [1]. In 
literature, it is known as concatenated codes [2], general 
concatenated codes [3] or super channel codes. The inner 
code is generally short and decoded with a soft decision 
decoding algorithm, while the outer code is generally 
longer and decoded with an algebraic decoding method 
[2].  
 
In most cases a convolutional code is used as an inner 
code in combination with a Reed Solomon code or another 
convolutional code as an outer code. Such a type of 
concatenated codes can be compared to the combination of 
codes investigated in this work (Fig.1). Two good 
characteristics are the result of such a concatenated 
schema: good error performance because of the use of 
SISO principle and good security performance as the 
result of the use of the cryptographic mechanisms. 
 
The next common point of this work with previous works 
in coding is the idea of the use of reliability in decoding. 
There are several works which explore the reliability-
based soft-decision decoding algorithms for linear block 
codes, using the concept of error correction by ordering 
the decoded bits by their reliability values. The values of 
soft outputs of the decoder have been used as reliability 
values.  
 
The idea of inversion of the least probable bits (with the 
lowest reliability values) originated from Chase decoding 
algorithms [4] in 1972, which were the generalization of 
the GMD (Generalized Minimum Distance) algorithms 
from 1966 [1]. These algorithms have been applied to a 
binary (n, k) linear block code and are referenced as LRP 
(Least Reliability Positions) algorithms. 
 
Chase algorithms generate a list of candidate code words 
by complementing all possible combinations of bits with 
the lowest reliability values. The candidate with the best 
metric is the decoded solution.  
 
(IJCSIS) International Journal of Computer Science and Information Security, Vol.1 No.1, May 2008 
 
 
- 2 - 
2 
The similarity to the method of the Soft Input Decryption, 
is the use of L-values reordered and iteratively tested. The 
difference is that Soft Input Decryption uses two decoders 
(inner and outer) and a non-linear block code 
(cryptographic algorithms). Two codes enable the use of 
feedback from the outer to inner code. 
 
The next group of algorithms, which use decoding based 
on ordering of L-values, is a group of MRIP (Most 
Reliable Independent Positions) - reprocessing decoding 
algorithms, as the Most Reliable Basis [MRB], the Least 
Reliable Basis [LRB] and the Ordered Statistic Decoding 
Algorithm [2].  
 
Joint source channel coding is the another topic related to 
this work. The cooperation between the source and 
channel decoder enables a better use of information of 
both decoders and better decoding results [5]. It is based 
on the turbo – principle, as well as Softbit - Source 
Decoding [6] and Iterative Source – Channel decoding [7]. 
The similarity to Soft Input Decryption is the use of 
iterative information exchange between the two elements 
of the receiver: channel and source decoder, in case of 
joint source channel coding, rsp. channel decoder and 
decryptor in case of Soft Input Decryption. 
 
2. Soft Input Decryption Algorithm 
Soft Input Decryption [8] is a method for the correction of 
SID blocks which contain cryptographic check values 
(digital signatures, MACs, H-MACs) by using L-values as 
the output of the SISO channel decoder. Cryptographic 
check values provide data 
integrity, data origin 
authentication and non repudiation [9].  
 
Soft Input Decryption works block oriented. The input for 
Soft Input Decryption contains data which are secured by 
cryptographic check values. The block which has to be 
corrected by Soft Input Decryption after channel decoding 
is called SID block (Soft Input Decryption block). It may 
contain data and cryptographic check values, or just 
cryptographic check values, depending on the used 
scenario (see Section 2.4).  
 
In Fig. 2 the  standard verification process without Soft 
Input Decryption is presented. 
 
 
 Fig. 2  Verification of a SID block without Soft Input Decryption. 
 
The algorithm of Soft Input Decryption (Fig. 3) is as 
follows: 
 
The Soft Input Decryption is successfully completed, if 
the verification of the cryptographic check value is 
successful, i.e. the output is “true”. If the verification is 
negative, the soft output of the channel decoder is 
analyzed and the bits with the lowest |L|-values are flipped 
(XOR 1). Then the decryptor performs the verification 
process and proves the result of the verification again. If 
the verification is negative, bits with another combination 
of the lowest |L|-values are changed. This iterative process 
will stop when the verification is successful or the needed 
resources are consumed. 
 
In the case that the attempts for correction fail, the number 
of modified bits is too large as a result of a very noisy 
channel, a very long SID block or an attack, so that the 
resources are not sufficient to find the correct content of a 
SID block.  
 
It may happen that the attempts for the correction of a SID 
block succeed, but the content of a SID block is not equal 
to the original one: a collision happened. This case has a 
negligible probability if the length of the cryptographic 
check values are chosen under security aspects (for 
example, considering the “birthday paradox”).  
 
(IJCSIS) International Journal of Computer Science and Information Security, Vol.1 No.1, May 2008 
 
 
Fig. 3  Algorithm of Soft Input Decryption. 
3. Simulations and Results 
The chosen length of the SID block is 320 bit. The reason 
for this length of a SID block is that this is a size of a 
digital signature based on Elliptic Curve Cryptography 
over GF(2160) or GF(p) with ld(p) = 160. Further on BPSK 
modulation, the model of an AWGN channel, as well as a 
convolutional and a turbo code [10] are used in the 
simulations. The used convolutional encoder has a code 
rate r = 1/2 and a constraint length m = 2. The turbo 
encoder with r = 1/3 is based on two parallel RSC 
convolutional encoders with r = ½ and a block interleaver 
of depth 17 [12]. The turbo decoder performs 3 iterations. 
The decoder (convolutional and turbo) uses a MAP 
algorithm [11]. The results in Fig. 4 are shown for Eb/N0 > 
1.5 dB. The simulations have been programmed in C/C++ 
programming language. For each point of the curves 
50.000 tests are performed which are sufficient to be 
representative. 
 
CCER (Cryptographic Check Error Rate) is defined as:  
 
blocks
SID
received
of
number
blocks
SID
incorrect
of
number
CCER =
  (1) 
 
An incorrect SID block is a SID block which could not be 
successfully verified or a SID block, which has been 
falsely successfully verified, i.e. a collision happened. 
Vice versa, a correct SID block is a successfully verified 
SID block and no collision happened, i.e. it is identical to 
the sent SID block. 
 
The complement of CCER is:  
blocks
SID
received
of
number
blocks
SID
correct
of
number
CCER
CCER
=
−
= 1
 (2) 
 
CCER is presented in Fig. 4 in relation to Eb/N0. Soft Input 
Decryption is performed for trials up to the 8, rsp. the 16 
lowest |L|-values (i.e. 28 rsp. 216 trials).  
 
The Soft Input Decryption gain [dB] means the reduction 
of CCER by Soft Input Decryption depending on Eb/N0. 
SID blocks can be successfully transmitted over a 
communication channel with Eb/N0 of 2.5 dB using Soft 
Input Decryption. For example, if 1 of 10 SID blocks 
cannot be verified (at 4 dB) without Soft Input 
Decryption, all SID blocks can be corrected in the case of 
convolutional codes. In case of a turbo code CCER can be 
reduced from 1/30 to 0 (at 2.5 dB).  
 
The results in Fig.5 are achieved for different lengths of 
SID blocks using convolutional coding: 128, 160, 320 and 
384 bits, with up to 16 flipped bits corresponding to the 
lowest positions of |L|-values. As expected, the coding 
gain of Soft Input Decryption is influenced by the length 
of a SID block: it is lower when a SID block is longer.  
  
In the following figures and sections a convolutional code 
is used only, because the simulations of convolutional 
codes are faster than of turbo codes and the coding gains 
of turbo codes are similar to those of convolutional codes 
(compare to Fig. 4). 
 
 
Fig. 4 Decrypting gain of 320 bit SID block [8] 
a) Convolutional code without Soft Input Decryption 
a) 
b) Convolutional code with Soft Input Decryption using up to the 8 
lowest |L|-values 
c) as b.), but using up to the 16 lowest |L|-values 
(IJCSIS) International Journal of Computer Science and Information Security, Vol.1 No.1, May 2008 
 
 
- 4 - 
4 
d)Turbo code without Soft Input Decryption 
e)Turbo code with Soft Input Decryption using up to the 8 lowest |L|-
values 
f)as e.), but using up to the 16 lowest |L|-values 
 
 
 
Fig. 5 CCER Coding gain of Soft Input Decryption using up to 16 lowest 
|L|-values, for different lengths of SID blocks  
 
4. Strategies of Soft Input Decryption 
The module “Changing of bits of SID block” (see Fig. 3) 
contains the strategy, in which sequence bits and 
combinations of bits of the SID block are changed, before 
the next verification is achieved. Depending on the 
strategy of Soft Input Decryption, different schedules of 
bit correction are possible.  
 
The static strategy of Soft Input Decryption is used for the 
results of Chapter 3. Proposals for other strategies are also 
given in this Chapter. 
 
4.1 Static Strategy 
 
If the first verification after starting Soft Input Decryption 
is not successful, the bit with the lowest |L|-value of the 
SID block is flipped, assuming that the wrong bits are 
probably those with the lowest 
|L|-values. If the 
verification is again not successful, the bit with the second 
lowest |L|-value is changed. The next try will flip the bits 
with the lowest and second lowest |L|-value, then the bit 
with the third lowest |L|-value, etc. The process is limited 
by the number of bits with the lowest |L|-values, which 
should be tested. The strategy follows a representation of 
an increasing binary counter, whereby the lowest bit 
corresponds to the bit with the lowest |L|-value, etc.  
 
The strategy is defined by following algorithm. 
 
The static strategy orders the bits of the SID block by their 
|L|-values starting with the lowest one and monotonly 
increasing. The output of the sort algorithm is represented 
as an example in Fig. 6. j is the increasing sequence of 
positions of |L|-values and Pj indicates the position of the 
bit with the jth lowest |L|-value in the original SID block. 
The length of the SID block is w. 
 
 
 
Fig. 6  Sorted sequence of bits of a SID block (an 
example). 
 
The function “Changing of bits of SID block” of the Soft 
Input Decryption algorithm (Fig. 2) is shown in Fig. 7 in 
detail. 
 
To control the strategy, an incrementing counter i = 1, …, 
2Nmax – 1 is used in binary representation of fixed lengths 
of Nmax with coefficients cij ∈ {0, 1}.  
                            ∑
=
−
=
max
1
1
, 2
N
j
j
j
i
c
i
                                 (3) 
Nmax is the maximum number of bits to be flipped, rsp. 
2Nmax – 1 is the maximum number of trials, if all 
verifications fail. Each value of the counter i describes one 
trial. The indices j of those coefficients cij which are 
marked (cij = 1) indicate the positions of L-values of the 
bits to be flipped. These positions can be found by using 
the sorted table as in Fig. 6.  
 
The sorted sequence Pj can be limited to PNmax. i is reset to 
0 at the beginning of Soft input Decryption. 
(IJCSIS) International Journal of Computer Science and Information Security, Vol.1 No.1, May 2008 
 
 
 
Fig. 7 Algorithm of the static strategy 
 
The strategy is based on the following assumption: if bits 
are wrong decoded by the channel decoder, than they have 
the lowest |L|-values. Unfortunately, this assumption is not 
true, because L-values are probability based and give only 
an orientation which bits may be wrong decoded. It may 
happen, for example, that combinations of up to 7 bits 
have to be tested, when only 3 bits are wrong. 
 
4.2 Dynamic Strategy 
 
The static strategy sorts the L-values of single bits. The 
dynamic strategy calculates the L-values of groups of bits 
to decide which trial should be performed next. It can 
happen, that a group of bits result in a lower |L|-value than 
a |L|-value of a single bit, i.e. that a specific group of bits 
is probably wrong. By this way, it is possible to find the 
group of wrong bits in only a few trials, not testing all 
combinations of flipped bits untill the bits untill the right 
combination is found like in the static strategy. The 
calculation is based on use of the L algebra [12] and much 
more complex than the static strategy. The elaboration of 
the dynamic strategy is for further study. 
 
4.3 BER Based Strategy 
 
The BER based strategy analyses, which number of errors 
is the most probable in the SID block, under consideration 
of Eb/N0 rsp. BER. To reduce the potential number of tests, 
L-values are taken into account. Example: if Nmax is 16 and 
4 bit errors are most probable for SID blocks of 320 bits, 
then up to 
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
4
16
 instead of 
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
4
320
tests are performed. If 
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
4
16
 tests are not successful, 
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
3
16
tests of 3 bit errors 
and 
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
5
16
tests of 5 bit errors have to be tested. The BER 
strategy is also for further study. 
 
5. Application Scenarios 
5.1 Scenario 1 
 
In scenario 1 (Fig. 7) digital signatures giving message 
recovery are used [13]. In this type of digital signatures 
the digital signature is not appended to the message, but 
contains the message, practically the digital signature 
replaces the message. 
 
If the verification process is successful, the message is 
also correctly recovered. The length of the message 
including redundancy is limited by the size of the 
underlying mathematical structure of the used asymmetric 
cryptography. For example, the length has to be shorter 
than 1024 bits, if RSA is used with a length of the 
modulus of 1024 bits, or shorter than 160 bits, if ECC 
(elliptic curve cryptography) is used over GF (2160). 
Algorithms can be found in [13] and [14]. 
 
This scenario can be often found in transaction oriented 
applications exchanging short messages, which have to be 
authentic. Typical examples are measurement values in 
industrial metering systems (electricity, water, gas etc.), 
data generated by sensors, as well as stock exchange rates.  
 
 
(IJCSIS) International Journal of Computer Science and Information Security, Vol.1 No.1, May 2008 
 
 
- 6 - 
6 
5.2 Scenario 2 
Scenario 2 (Fig. 8) considers signatures with appendix 
[15]. Messages signed by signatures with appendix have 
arbitrary lengths, but Soft Input Decryption can only be 
applied to SID blocks of limited lengths (Note: the 
application of a collision free one-way hash function is 
considered here to be part of the signature generation and 
verification process). In this scenario, it is assumed that 
the message and the signature are transmitted separately 
and the SID block consists only of the signature: the 
message is transmitted via a communication channel 
different from the one used for the transmission of the 
digital 
signature 
(outband), 
or 
via 
the 
same 
communication channel (inband). The message itself is 
transmitted first and – if modified during transmission – 
corrected by redundancy within the message, by repetition 
or by agreement of the communication partners. So, it is 
assumed that finally the message is received correctly by 
the receiver. The digital signature 
is 
transmitted 
afterwards, either when it is generated on request or when 
the action described by the message should be executed.  
 
Typical examples are legal contracts or bank transactions, 
which are prepared in advance, and the digital signature is 
transmitted at the requested moment. If an error occurs 
during the signature verification, the signature is not 
correct: it has been manipulated or errors occurred during 
the transmission, which can not be corrected by the 
channel decoder. 
 
In this case, the Soft Input Decryption block consists of 
one signature block used for verification of the message.  
 
 
 
Fig. 8 Scenario of signatures with appendix 
 
 
5.3 Scenario 3 
Scenario 3 (Fig. 9) is the most general scenario and 
considers messages with a cryptographic check value: 
MAC [16], H-MAC [17] or digital signatures with 
appendix.  
 
In this case, the SID block consists of a message extended 
by a cryptographic check value.  
 
Typical examples are credit/debit applications and other 
bank applications. 
 
At one hand, from the point of view of Soft Input 
Decryption it does not matter which scenario is applied. 
Soft Input Decryption always tries to correct the SID 
block as long as the verification fails. At other hand it is 
interesting to show that there are many aplications for Soft 
Input Decryption, even if the lengths of SID blocks are 
relativly short. 
 
6. Performance aspects of L-values 
6.1. The number of L-values required for correction 
 
If the performance of Soft Input Decryption should be 
estimated, at first it is necessary to consider the reliability 
of the soft input. 
 
Fig. 10 shows the number of L-values needed for 
correction of 95 % of SID blocks for different lengths of 
SID blocks: w = 128, 160, 320 and 384. 
In case of SID blocks of length of 320 bits the usage of up 
to 8 L-values is sufficient for the correction if Eb/N0 > 4 
dB. The number of L-values necessary for correction 
increases exponentially with decreasing of S/N: for Eb/N0 
< 3.5 dB 13 L-values are needed for 95 % correction.  
 
Fig. 10 Number of L-values needed for correction of 95 % of SID blocks  
 
 
6.2. The theoretical minimum needed for correction  
 
The problem is that reliability values themselves are not 
reliable. So, the question arises, which is the number of 
errors in a SID block, which is the lower limit of L-values 
to be used by Soft Input Decryption.  
(IJCSIS) International Journal of Computer Science and Information Security, Vol.1 No.1, May 2008 
 
 
The probability Pw,i , that a code word of length w – in this 
case a SID block – contains i errors is: 
 
                          
i
w
i
i
w
p
p
i
w
P
−
−
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
)
1
(
,
                    (4) 
where p represents BER. 
 
Soft Input Decryption tests all possible combinations of up 
to Nmax L-values. The probability Pw that, after correction 
by Soft Input Decryption, only errors which are longer 
than Nmax will not be corrected is [18]: 
 
                                                                 
∑
+
=
−
−
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
w
N
i
i
w
i
w
p
p
i
w
P
1
max
)
1
(
                                                        
(5) 
 
Soft Input Decryption corrects the data received from 
channel decoding. Therefore p means the bit error rate 
after the channel decoder. p depends on the quality of a 
MAP decoder. 
 
In the case of 95 % corrected SID blocks, Pw = 0.05. 
                                 
∑
∑
+
=
=
−
−
−
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−
=
−
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
≥
w
N
i
N
i
i
w
i
i
w
i
w
p
p
i
w
p
p
i
w
P
1
0
max
max
)
1
(
1
)
1
(
05
.
0
(6) 
 
Nmax is calculated for the correction of more than 95 % 
errors has been done for lengths of SID blocks of w = 
{128, 160, 320, 384} bits (Fig. 11). 
 
Nmax  in (5) and (6) means the minimum Nmax because the 
case considers the number of L-values for correction of Pw  
wrong bits. 
 
The results are shown in Fig. 11. 
 
 
 
Fig. 11 Theoretically minimum number of bits (minNmax) to be changed  
 
Now, the results of Fig. 10 and 11 can be compared. Fig. 
12 shows the comparison for SID block of 320 bits. The 
reason for the significant difference is the incorrect 
allocation of |L|-values compared to wrong bits, due to 
imperfections in the implementation of MAP decoding 
algorithm. 
 
 
Fig. 12 Comparison of needed and theoretical number of L-values for 
SID block of the length 320 bits 
 
6.3. Estimation of the number of L-values for the 
correction of long SID blocks 
 
In this section the number of needed L-values for the 
correction of SID blocks longer than 384 bits is 
considered, because the application of Soft Input 
Decryption of longer SID blocks seems to be very 
interesting (see Scenario 3 of Section 2.4 or consider RSA 
digital signatures instead of ECC which will be discussed 
later in this section). The estimation for the number of 
required |L|-values is done by interpolation of the results 
for SID blocks of lengths of 128, 160 and 320 bits and 
extrapolation for longer SID blocks. The results for 384 
bits known by simulations are used for the verification of 
the extrapolation. 
 
Fig. 13 (w = 320, Eb/N0 = 3 dB) shows the percentage of 
corrected SID blocks per |L|-value: 20 % of SID blocks 
are corrected with the lowest |L|-value. Additional 13 % 
are corrected with the second lowest |L|-value; with the 
third lowest |L|-value additional 11 % etc…; with the 15th 
lowest |L|-value additional 1 % more SID blocks are 
corrected than with the 14th lowest |L|-value.  
(IJCSIS) International Journal of Computer Science and Information Security, Vol.1 No.1, May 2008 
 
 
- 8 - 
8 
  
Fig. 13 The percentage of corrected SID blocks per |L|-value 
  
The percentage of corrected SID blocks per |L|-value is 
tested for lengths of 128, 160 and 320 bits and for 
different Eb/N0. The results of tests show curves with a 
negative exponential function of the form (see Fig. 13): 
 
 y = k e-ax                                      (7) 
 
Coefficients k and a depend on the length w of the SID 
block and Eb/N0. This dependence is derived in this section 
and then applied for other values.  
 
As the total percentage of corrected SID blocks is 100 % 
after testing of all L-values, the following condition is 
valid: 
1
1
)1
(
1
1
=
−
−
=
=
−
−
−
=
−
=
∑
∑
a
aw
a
w
i
ai
w
i
i
e
e
ke
e
k
y
        (8) 
 
or, by presenting e-ai as an infinite sum: 
                                                        
aw
aw
i
i
aw
aw
aw
a
e
a
e
i
a
e
a
a
a
e
a
a
a
e
e
k
−
−
∞
=
−
−
−
−
≈
−
=
−
+
+
+
=
−
−
+
+
+
+
=
−
−
=
∑
1
1
!
1
...
!
3
!
2
1
1
...
!
3
!
2
1
1
1
1
3
2
3
2
(9) 
 
The negative exponential function is derived for w = {128, 
160, 320} and Eb/N0 = [1, 5.5] dB in steps 0.5 dB. For 
each function a and k are derived approximately and 
shown in Table 2. 
 
The relation between the exponent a and Eb/N0 is observed 
in the next step. S/N is used instead of Eb/N0, respecting 
the code rate of  ½: 
                                                                         
dB
N
E
N
S
b
3
0
−
=
                       (10) 
 
Approximations are done using S/N ratio which is easier 
for calculation. The entries of the first and third row of 
Table 2 is used for approximation by a second order 
polynomial:                      
                        
C
N
S
B
N
S
A
a
+
⎟
⎠
⎞
⎜
⎝
⎛
+
⎟
⎠
⎞
⎜
⎝
⎛
=
2
            (11) 
 
The calculated coefficients A, B and C are shown in Table 
2 for SID blocks of length of 128, 160 and 320 bits. The 
approximation of the dependence of a on S/N is shown in 
Fig. 14. 
 
The coefficients A, B and C have different values 
dependent on the length of SID blocks. A, B and C show a 
linear relation to w. Therefore A, B and C are 
approximated by linear functions of w.  
 
A = A(w) = KA ۔ w + NA                          (12) 
 
  B = B(w) = KB ۔ w + NB                          (13) 
                                                                
C = C(w) = KC ۔ w + NC                          (14) 
 
The values of the linear coefficients are shown in Table 3. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
(IJCSIS) International Journal of Computer Science and Information Security, Vol.1 No.1, May 2008 
 
 
Eb/N0 [dB] 
1 
1.5 
2 
2.5 
3 
3.5 
4 
4.5 
5 
k 
0.083 
0.127 
0.271 
0.323 
0.418 
0.461 
0.646 
0.733 
0.821 
 
w = 128 
a 
0.08 
0.12 
0.24 
0.28 
0.35 
0.38 
0.5 
0.55 
0.6 
k  
0.030 
0.078 
0.127 
0.221 
0.284 
0.47 
0.582 
0.792 
1.059 
 
w= 160 
a 
0.038 
0.075 
0.12 
0.2 
0.25 
0.38 
0.46 
0.6 
0.7 
 k  
0.02 
0.025 
0.062 
0.221 
0.258 
0.419 
0.733 
1.222 
1.454 
 
w = 320 
a  
0.02 
0.025 
0.06 
0.2 
0.23 
0.35 
0.5 
0.8 
0.9 
 
Table 1 Coefficients k and a for SID block of w = 128, 160 and 320 bit
 
 
 
 
 
 
 
 
 
 
 
 
 
Table 2 Coefficients A, B and C 
 
KA 
NA 
KB 
NB 
KC 
NC 
-0.00002 
0.043 
-0.00015 
0.225 
-0.00025 
0.32 
 
Table 3 Values of linear coefficients KA, NA, KB, NB, KC and NC of coefficients A, B and C  
 
 
Fig. 15 Coefficient a in dependence on Eb/N0 for different lengths of SID 
block 
 
Using equations (7) and (9), the percentage of corrected 
bits (indicated as y in (7)) can be calculated as a function 
of positions of |L|-values (indicated as x in (7)), S/N and 
the length w of a SID block: 
                        
x
w
N
S
a
w
w
N
S
a
w
N
S
a
ax
e
e
e
ke
y
)
,
/
(
)
,
/
(
)
,
/
(
1
1
−
−
−
−
−
=
=
       (15) 
 
with 
 
                              
)
(
)
(
)
(
)
(
)
(
)
(
,
2
2
NC
w
KC
N
S
NB
w
KB
N
S
NA
w
KA
w
C
N
S
w
B
N
S
w
A
w
N
S
a
+
⋅
+
⎟
⎠
⎞
⎜
⎝
⎛
⋅
+
⋅
+
⎟
⎠
⎞
⎜
⎝
⎛
⋅
+
⋅
=
+
⎟
⎠
⎞
⎜
⎝
⎛
⋅
+
⎟
⎠
⎞
⎜
⎝
⎛
⋅
=
⎟
⎠
⎞
⎜
⎝
⎛
(16) 
 
w 
128 
160 
320 
A 
0.04 
0.04 
0.037 
B 
0.206 
0.201 
0.177 
C 
0.288
0.28
0.24 
(IJCSIS) International Journal of Computer Science and Information Security, Vol.1 No.1, May 2008 
 
 
- 10 - 
10 
If the number of |L|-values needed for correction are 
indicated by x, a normalized distribution function of 
percentage of correction by xth L-value y can be expressed, 
using equation (16), as: 
 
(
)
(
)
(
)
(
)
⎪⎭
⎪
⎬
⎫
⎪⎩
⎪
⎨
⎧
⋅
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
+
⋅
+
⎟
⎠
⎞
⎜
⎝
⎛
⋅
+
⋅
+
⎟
⎠
⎞
⎜
⎝
⎛
+
⋅
−
−
−
⎪⎭
⎪
⎬
⎫
⎪⎩
⎪
⎨
⎧
⋅
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
+
⋅
+
⎟
⎠
⎞
⎜
⎝
⎛
+
⋅
+
⎟
⎠
⎞
⎜
⎝
⎛
+
⋅
−
⋅
⋅
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
+
⋅
+
⎟
⎠
⎞
⎜
⎝
⎛
⋅
+
⋅
+
⎟
⎠
⎞
⎜
⎝
⎛
⋅
+
⋅
=
−
≈
−
−
w
NC
w
KC
N
S
NB
w
KB
N
S
NA
w
KA
x
NC
w
KC
N
S
NB
w
KB
N
S
NA
w
KA
NC
w
KC
N
S
NB
w
KB
N
S
NA
w
KA
e
ae
y
aw
x
a
)
(
)
(
)
(
exp
1
)
(
)
(
)
(
exp
)
1
/(
2
2
2
*
 
(17) 
                                                                                                                                                                                  
If the number x0 of L-values needed for correction of y(x0) 
percentage of errors has to be, equation (7) is expressed 
as: 
 
                                           
∑
∑
=
−
−
−
−
−
=
−
−
=
−
−
=
≈
0
0
0
1
*
1
0
1
1
1
1
)
(
x
i
aw
ax
ax
aw
a
x
a
x
i
e
e
e
e
e
e
k
x
y
 (18) 
 
and x0 is found as: 
 
                                                         
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−
−
≈
−
)
1
)(
(
1
1
ln
1
0
0
aw
e
x
y
a
x
               (19) 
 
It is noted that equation (19) is based on an interpolation 
of Eb/N0 = [1, 4] dB (i.e. S/N = [-2, 2] dB) and w = [128, 
160, 320].  
 
y(x0) can be between 0 and 100 [%], but it is 95 % in this 
paper. 
 
The maximum position of minimum |L|-value can be 
found for different lengths of SID blocks and different 
Eb/N0.  
 
In order to check equation (19), y(x0) (needed L-values) 
for correction of 95% SID blocks of length of 384 bits 
(extrapolation) are compared to the results of tests (Fig. 
16): 
 
 
 
 
 
 
Fig. 16 Comparison of L-values needed for correction of 95% of  SID 
blocks (w = 384) based on equation (19) and simulations (Fig. 10)  
 
Fig. 16 shows that equation (19) can be trusted and used 
for further extrapolations. 
 
Equation (19) is now applied for SID blocks of length w = 
1024 in Fig. 17. The length of 1024 bits is chosen for 
comparison, because RSA signatures with a signature 
length of 1024 bits offer the same security level as digital 
signatures based on ECC with the signature length of 320 
bits. It may appear attractive to use RSA signatures 
because the verification time is very short when a public 
exponent with a low Hamming weight is used.  
 
Assuming Eb/N0 = 3 dB, the number of L-values is 48 
compared to 14 when using ECC digital signatures of 320 
bit. Therefore, at one hand, it becomes clear, that the use 
of RSA digital signatures is not suitable for Soft Input 
Decryption. At the other hand, the application of Soft 
Input Decryption to longer blocks than 1024 bits is 
realistic if Eb/N0 is not too low. 
 
 
Fig. 17 Comparison of L-values needed for correction of 95% of  SID 
blocks with w = 320 and w = 1024 
 
(IJCSIS) International Journal of Computer Science and Information Security, Vol.1 No.1, May 2008 
 
Fig. 17 shows that 48 L-values rsp. 248 tests are necessary 
in the case of RSA digital signatures are needed compared 
to 14 rsp. 214 tests in case of ECC digital signatures. 
 
7. Time Performance 
 
Under practical aspects it is important to consider the 
consumed resources of Soft Input Decryption, specifically 
the time needed for the correction of SID blocks. The 
needed time depends on the cryptographic algorithm and 
on the number of L-values which are necessary to correct 
the errors. Therefore the success of Soft Input Decryption 
is highly dependent on the quality of the soft output of the 
channel decoder. 
 
The time needed to perform 28 verifications of digital 
signatures of 320 bits with appendix (based on ECDSA) 
without hash calculation which are not necessary in 
Scenario 2, MACs (CBC MAC – DES with key size of 56 
bit) and H-MACs (SHA-1 with output size of 160 bit) are 
shown in Table 3 – 5. The numbers are based on use of a 
PC with Pentium 4 of 1.7 and 1.8 GHz [19].  
 
The second row of the tables shows the number of 
verifications and consumed time, which is needed for 
testing and correcting bits with up to the 8 lowest |L|-
values. In the case of MAC/H-MAC a new MAC/H-MAC 
is computed, if the changed bit is in the message part. If 
the changed bit is in the MAC/H-MAC part, only a 
comparison to the previously computed MAC/H-MAC is 
performed, which costs almost no time. It is assumed that 
the L-values used for correction are equally distributed 
over the message part and the cryptographic check value.  
 
In the table with the results of digital signatures (Table 3) 
there is an additional third row which assumes an 
optimization of the digital signatures verifications (100 
times faster verification) following the first verification. 
The arithmetic of subsequent verifications is much more 
efficient and faster, if only one bit of the input of  the 
verification is changed compared to one of the preceding 
verifications because only a single point addition has to be 
executed for correction. Example: in the case of ECKDSA 
[13] only one single point addition is necessary for 
correction.  
 
The most interesting result is that digital signatures are 
more suitable for Soft Input Decryption than MAC and H-
MAC, if the assumption, that succeeding verifications 
need only 1 % of the first one, is true. Even if succeeding 
verifications need less than 25 % of the first one, Soft 
Input Decryption with digital signatures is faster than Soft 
Input Decryption with H-MACs or MACs.  
 
 
 
Number 
of 
Verifications 
Time [s]  
1,7 GHz 
Time [s]  
1,8 GHz
1 1 
0.0049 
0.0044 
2 256  
1.2544 
1.1264 
3 1st 
 + 255 
similar 
0.0174 
0.0156 
 
Table 3 Computation times for verification of digital 
signatures 
 
 
Number 
of 
Verifications 
Time [s]  
1,7GHz 
Time [s]  
1,8 GHz
1 1 
0.002 
0.00187 
2 256 * m / (m + n)  0.3072 
0.2872 
 
Table 4 Computation times for verification of  MACs (n = 
128 bits) of a message (m = 192 bits) 
 
 
Number 
of 
Verifications 
Time [s]  
1,7 GHz 
Time [s]  
1,8 GHz
1 1 
0.00424 0.004 
2 256 * m / (m + n)  0.543 
0,512 
 
Table 5 Computation times for verification of H-MACs (n = 160 bits) of 
a message (m = 160 bits) 
 
8. Conclusion and Further Work 
 
In this paper the principles of Soft Input Decryption are 
presented, as well as results of various simulations. The 
application of the Soft Input Decryption method is shown 
using different 
scenarios. The 
coding gain of 
cryptographic check error rates which is more than 2 dB in 
case of SID blocks of length of 320 bits show that Soft 
Input Decryption 
is a promising method which 
characteristics have to be examined for further use and 
improvement. 
 
Different strategies for changing of bits are possible, 
depending on a used system and error distribution. In this 
paper a static strategy is used, but also other possible 
strategies as dynamic and BER strategy are mentioned. 
These and other suggestions for new strategies are for 
further study. 
The performance of L-values is analyzed by comparison of 
results of tests and theoretical calculations. It is shown that 
the L-values are not reliable, because bits with lower |L|-
(IJCSIS) International Journal of Computer Science and Information Security, Vol.1 No.1, May 2008 
 
 
- 12 - 
12 
values are not necessarily wrong bits. For that reason 
much more L-values have to be tested, than it would be 
necessary if the wrong bits would really have the lowest 
|L|-values. Results show that L-values become less reliable 
with decreasing of Eb/N0. 
 
Existing results of performances of L-values (for SID 
blocks of length of 128, 160 and 320 bit) are used for 
generation of equations which approximately find the 
number of needed L-values for the correction of defined 
percentage of SID blocks. Results of approximation are 
confirmed by comparison to the known results of tests for 
SID blocks of length of 384 bits. By extrapolation of 
calculated equations on SID blocks of length 1024 bit, the 
number of needed L-values has been calculated, instead of 
performing of long Soft Input Decryption tests. 
 
Time performance of Soft Input Decryption depends on 
used cryptographic mechanisms (digital signature, MAC 
or H-MAC). The surprising results is that digital 
signatures show very good performance results when the 
time needed for verification of “neighboured” signatures is 
improved.  
 
The future work should focus on improvement of 
arithmetical efficiency of cryptography for Soft Input 
Decryption to achieve faster verification process in a 
scope of Soft input Decryption and to prove the 
assumption used in row 3 of Table 3. 
 
Section 3.2 more sophisticated strategies of Soft Input 
Decryption instead of static strategy have been outlined. 
Further studies will elaborate these strategies and test the 
performance. 
 
Investigation of Soft Input Decryption should be also 
applied to standardized turbo codes for 3G, using the fact 
that the remaining errors after turbo coding are very often 
grouped (flipping of corresponding groups of bits). 
 
References 
[1] Forney, G.D.Jr., Concatenated Codes, MIT Press, Cambridge, 1966. 
[2] Lin, S., Costello, D.J., Error Control Coding, Pearson Prentice Hall, 
USA, 2004. 
[3]  Bossert, M., Kanalcodierung, B. G. Treubner, Stuttgart, 1998. 
[4] D. Chase, A Class of Algorithms for Decoding Block Codes with 
Channel Measurement Information, IEEE Trans. Inform. Theory, IT-
18, pp. 170-182, January 1972.  
[5] Hagenauer, J.: Source-Controlled Channel Coding, IEEE Trans. On 
Communications, pp. 2449-2457, September 2004. 
[6]  Adrat, M., Picard, J.-M., Vary, P., Analysis of extrinsic Information 
from softbit-source decoding applicable to iterative source-channel 
decoding, in Proc. For ITG Conference 2002 – Source and Channel 
Coding, Berlin, January 2002. 
[7]  Görtz, N., Iterative Source-Channel Decoding by Channel Coded 
Optimal Estimation, Proc. Of 3rd ITG Conference Source and 
Channel Coding, Munich, Germany, pp. 267-272, January 2000 
[8] Živić, N., Ruland, C., Softinput Decryption, 4th Turbocode 
Conference, 6th Source and Channel Code Conference, VDE/IEEE, 
Munich, April 3 – 7, 2006 
[9] Ruland, C., Informationssicherheit in Datennetzen, datacom Verlag, 
Bergheim 1993, ISBN-3-89238-081-3 
[10] Berrou, C., Glavieux, A., Thitimajshima, P., Near Shannon Limit 
Error Correcting Coding and Decoding: Turbo Codes, Proc. IEEE 
International Conference on Communication, Geneva, Switzerland, 
vol. 2/3, pp. 1064-1070, 1993 
[11] Bahl, L., Jelinek, J., Raviv, J., Raviv, F., Optimal decoding of linear 
codes for minimizing symbol error rate, IEEE Transactions on 
Information Theory, IT-20, pp. 284-287, March 1974. 
[12] Fu – Hua Huang, Evaluation of Soft Output. Decoding for Turbo 
Codes, thesis at the Faculty of the Virginia Polytechnic Institute, 
May 
1997., 
http://scholar.lib.vt.edu/theses/available/etd-71897-
15815/unrestricted/ 
[13] ISO/IEC 15946-4, Information technology – Security techniques – 
Cryptographic Techniques based on Elliptic Curves – Part 4: 
Digital signatures giving message recovery, 2004. 
[14]  ISO/IEC 14888-3: Information technology – Security techniques – 
Digital signatures giving message recovery – Part 3:  
[15]  ISO/IEC 14888-1, Information technology – Security techniques – 
Digital signatures with appendix – Part 1: General, 1998. 
[16]  ISO/IEC 9797-1, Information technology – Security techniques – 
Message Authentication Codes (MACs) – Part 1: Mechanisms 
using a block cipher, 1999. 
 [17] ISO/IEC 9797-2: Information technology – Security techniques -   
Message Authentication Codes (MACs) – Part 2: Mechanisms 
using a hash-function, 2000 
[18]   Drajić, D.B.: Uvod u teoriju informacija i kodovanje, Akademska 
misao, Beograd, 2004  
[19] Performance of optimized Implementations of the NESSIE 
Primitives, NESSIE Project Report, Version 2, 2003 
 
Natasa Zivic, Dr., born 1975 in Belgrade, 
Serbia, graduated from the Faculty of 
Electrical 
Engineering 
(Electronics, 
Telecommunication and Automatics) of 
the Belgrade University in 1999. at the 
Telecommunication Department. After 
the Post diploma studies at the same 
Faculty (Telecommunications Division) she defended her 
Magister Thesis (Acoustics) in 2002. 
From October 2004. she was scientific assistant at the 
University of Siegen in Germany at the Institute for Data 
Communications Systems as a DAAD and University of 
Siegen Scholarship holder. In 2007. she defended her 
Doctoral Thesis on the same University. The main course 
of her work in Siegen is Coding and Cryptography. 
From 2000. till 2004. she was working at the Public 
Enterprise of PTT “Serbia”, Belgrade as the senior 
engineer. Currently she is employed as an Assistant 
Professor 
at 
the 
University 
of 
Siegen. 
 
 
(IJCSIS) International Journal of Computer Science and Information Security, Vol.1 No.1, May 2008 
 
 
 
Fig. 1  Communication System using Concatenated Codes. 
 
 
Fig. 7 Scenario of signatures giving message recovery 
 
 
 
Fig. 9 Scenario of messages with cryptographic check values 
(IJCSIS) International Journal of Computer Science and Information Security, Vol. 1, No. 1, May 2009 
 
22
AUTOMATIC DEFECT DETECTION AND 
CLASSIFICATION TECHNIQUE FROM 
IMAGE: A SPECIAL CASE USING CERAMIC 
TILES 
G. M. Atiqur Rahaman1 
1Computer Science and Engineering Discipline       
Khulna University 
Khulna 9208, Bangladesh 
atiq99@hotmail.com                                                                                                             
Md. Mobarak Hossain2 
2Computer Science and Engineering Department       
Asian University of Bangladesh 
 Dhaka, Bangladesh 
mobarak10jan@yahoo.com 
 
 
Abstract—Quality control is an important issue in the ceramic tile 
industry. On the other hand maintaining the rate of production with 
respect to time is also a major issue in ceramic tile manufacturing. 
Again, price of ceramic tiles also depends on purity of texture, 
accuracy of color, shape etc. Considering this criteria, an 
automated defect detection and classification technique has been 
proposed in this report that can have ensured the better quality of 
tiles in manufacturing process as well as production rate. Our 
proposed method plays an important role in ceramic tiles industries 
to detect the defects and to control the quality of ceramic tiles. This 
automated classification method helps us to acquire knowledge 
about the pattern of defect within a very short period of time and 
also to decide about the recovery process so that the defected tiles 
may not be mixed with the fresh tiles.  
Keywords-: Quality Control; Pattern of Defect; Defected 
Ceramic Tiles; Fresh Tiles 
I. 
 INTRODUCTION  
 Image processing is one of the mostly increasing areas in 
computer science. As technology advances, the analog imaging 
is switched to the digital system now-a-days. Every day, we 
capture huge amount of images which are very difficult to 
maintain manually within a certain period of time. So the 
concept and application of the digital imaging grows rapidly. 
Digital image processing is used to extract various features 
from images. This is done by computers automatically without 
or with little human intervention. One of the most important 
operations on digital image is to identify and classify various 
kinds of defects. Thus to detect the defects from any image 
some methods are established and placed at three levels. At the 
lowest level, some techniques are available which deal directly 
with the raw, possibly noisy pixel values, with de-noising and 
edge detection being good examples. In the middle there are 
algorithms which utilize low level results, such as segmentation 
and edge linking. At the highest level are those methods which 
attempt to extract semantic meaning from the information 
provided by the lower level.  
Ceramic tiles industry sector is now a very important sector 
for manufacturing the ceramic tiles. All production phases are 
technically maintained until 
the 
final 
stage of 
the 
manufacturing process appeared. Sometimes checking is 
needed for the ceramic tiles if they are able to serve customer 
needs, i.e. to find defected tiles. So it is an important task to 
categorize the ceramic tiles after production based on surface 
defects. The manual method of defects inspection is labor 
intensive, slow and subjective. Although automated sorting and 
packing lines have been in existence for a number of years, the 
complexity of inspecting tiles for damage and selecting them 
against the criteria of a manufacturer i.e. automated defected 
tiles inspection have not been possible. Again human judgment 
is influenced by expectations and prior knowledge. In many 
detection tasks for example, edge detection, there is a gradual 
transition from presence to absence. On the other hand, in 
“obvious” cases, most naive observers agree that the defect is 
there, even when they cannot identify the structure. Such a 
monitoring task is of course tedious, subjective and expensive. 
For all these reason no one can deny the significance of 
automated defect detection and classification system.  
The objective of our research is to propose an efficient 
defect detection and classification technique which will be able 
to find out image defects at a high rate within a very short time.  
The overall outline of this paper is mentioned as follows. 
Section 2 reviews the existing works briefly. Section 3 
illustrates our proposed techniques. Section 4 presents the 
experimental results and comparison. Finally, the conclusion is 
presented in Section 5. 
II. 
 EXISTING METHODS FOR DEFECT DETECTION  
 In the previous years, some proposed defect detection 
methods have been proposed to find out the image defects. But 
they have some limitations that can be described briefly as 
follows: 
In [3], H. Elbehiery et al. presented some techniques to 
detect the defects in the ceramic tiles. They divided their 
method into two parts. In the first part, Existing method 
consisted with the captured images of tiles as input. As the 
output, they showed the intensity adjusted or histogram 
equalized image. After that, they used the output of first part as 
input for the second part. In the second part of their algorithm, 
(IJCSIS) International Journal of Computer Science and Information Security, Vol. 1, No. 1, May 2009 
 
23
different 
individual 
complementary 
image 
processing 
operations have been used in order to identify various kinds of 
defects. Prevailing task emphasized on the human visual 
inspection of the defects in the industry. But their system is not 
automated which is very much necessary in the manufacturing 
process. Again their proposed method is operation redundant 
because they apply their second part on every test image to 
identify various types of defects. Moreover, their proposed 
method is very time consuming. 
In [4], C. Boukouvalas et al. concerned about the problem 
of automatic inspection of ceramic tiles using computer vision. 
They applied techniques for pinhole and crack detectors for 
plane tiles based on a set of separable line filters, through 
textured tile crack detector based on the wigner distribution and 
a novel conjoint spatial-spatial frequency representation of 
texture, to a color texture tile defect detection algorithm which 
looks for abnormalities both in chromatic and structural 
properties of texture tiles. But, using separate filtering 
techniques for different types of defects is not a good idea at 
all, because in such case high computational time is a major 
issue for applying a large number of operations. Again, their 
procedure is an automated visual inspection system where they 
only show the defects making them clear to detect the defects 
found on image.  
In [5], Se Ho Choi et al. presented a real time defect 
detection method for high speed bar in coil. To enhance the 
performance of the detection they used edge preserving method 
for noise reduction, to separate images with different gray 
levels they used the laplacian filter (2nd differential) and after 
that they used double thresholding to binarize the image. But 
the major drawback of their process is that their method will 
not be able to find the orientation of the edge because of their 
using of laplacian filter, according to [7] which will be needed 
for the defect of ceramic tiles. The technique using the 
laplacian filter malfunctions for corner and curves. 
We generally have found total eight types of defects from 
the existing defect detection methods. These types of defects 
are shown in the following Table I. 
TABLE I.  
 TYPES OF CERAMIC TILE DEFECTS 
Name of 
Defects 
Description 
Crack 
Break down of tile
Pinhole 
Scattered isolated black-white 
pinpoint spot 
Blob 
Water drop spot on tile surface
Spot 
Discontinuity of color on surface
Corner 
Break down of tile corner
Edge 
Break down of edge
Scratch 
Generally scratch on surface
Glaze 
Blurred surface on tile
A. Maintaining the Integrity of the Specifications 
The template is used to format your paper and style the text. 
All margins, column widths, line spaces, and text fonts are 
prescribed; please do not alter them. You may note 
peculiarities. For example, the head margin in this template 
measures proportionately more than is customary. This 
measurement and others are deliberate, using specifications that 
anticipate your paper as one part of the entire proceedings, and 
not as an independent document. Please do not revise any of 
the current designations. 
III. 
 MATERIALS AND METHODS  
A. 
 Proposed Approach For Defect Detection And 
Classification 
The complete flow chart of our proposed defect detection 
and classification technique has been rendered in the following 
Fig.  1. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure  1.  Flow Chart of the Proposed Method 
 
 
In this section, we propose a new method for defect 
detection and classification. It can make the performance of 
defect detection rate higher than the existing one and can 
reduce the total computational time. Here, a common sequence 
of operations is applied to detect different types of defects in 
ceramic tiles and some proposed algorithms are employed to 
classify them. The proposed defect detection and classification 
approach will be performed using the following three steps: 
Yes
No
Morphological 
Operation
Saving Image 
as Matrix
Image Acquisition 
Image Enhancement 
Noise Reduction 
Edge Detection 
Is Defect 
Detection 
Successful? 
Final Result 
Defect  
Classification 
Start 
(IJCSIS) International Journal of Computer Science and Information Security, Vol. 1, No. 1, May 2009 
 
24
Step 1: Performing some image preprocessing operations. 
Step 2: Applying the proposed defect detection process. 
Step 3: Classifying the defect using all proposed 
algorithms. 
B. 
 Performing Some Image Preprocessing Operations 
At first, we have to employ some image preprocessing 
operations on the input image before applying the proposed 
defect detection process. Preprocessing steps are necessary for 
converting the captured RGB image found from the real source 
so that they can be eligible for performing any binary 
operations onto it. In our proposed method, we apply some 
preprocessing steps such as image enhancement, noise 
reduction etc. Again, at every preprocessing step we have a lot 
of options for using various kinds of methods in different 
applications.  
1) 
 Image Acquisition 
Image acquisition is the process of obtaining a digitized 
image from a real world source. Each step in the acquisition 
process may introduce random changes into the values of 
pixels in the image which is referred to as noise. A ceramic tile 
image is captured and stored into the computer for further 
processing. This may be achieved by taking a photograph with 
a conventional camera, having the film made into a print and 
scanning the print into a computer. In our method, we have 
used SAMSUNG DIGIMAX-W54 digital camera for image 
capturing. Then, this image is trimmed with        m ×  n (width 
and height) to make all the images to equal size. 
2) 
 Image Enhancement 
Actually, image enhancement technique is to make the 
image clearer so that various operations can be performed 
easily on the image. For this, at first the captured RGB image is 
converted to the gray level image. Contrast stretching (often 
called normalization) is a simple image enhancement technique 
that attempts to improve the contrast in an image by stretching' 
the range of intensity values it contains to span a desired range 
of values, e.g. the full range of pixel values that the image type 
concerned allows. Low contrast images can be found due to the 
poor illumination, lack of dynamic range in the imaging sensor, 
or due to the wrong setting of the lens. The idea behind the 
contrast stretching is to increase the dynamic range of intensity 
level in the processed image. 
 The general process of the contrast stretching operation [1] 
on grayscale image is to apply the following equation on each 
of the pixels in the input image to form the corresponding 
output image pixel:  
i
n
y
x
I
y
x
O
i
+
−
−
=
)
min
max
min)(
)
,
(
(
)
,
(
 
where, O(x,y) represents the output image, I(x,y) represents 
the xth pixel in the yth column in the input image. In this 
equation, ni represents the number of intensity levels, i 
represents the initial intensity level, "min" and "max" represent 
the minimum intensity value and the maximum intensity value 
in the current image respectively. Here "no. of intensity levels" 
shows the total number of intensity values that can be assigned 
to a pixel. For example, normally in the gray-level images, the 
lowest possible intensity is 0, and the highest intensity value is 
255. Thus "no. of intensity levels" is equal to 256. The contrast 
stretching operation is applied on the grayscale images in two 
passes. In the first pass the algorithm calculates the minimum 
and the maximum intensity values in the image, and in the 
second pass through the image, the above formula is applied on 
the pixels.  
In the proposed method, we enhance the gray level image to 
improve its visual quality and machine recognition accuracy 
using the following formula, described in [1]: 
(
)
E
M
h
stretc
F
INTRANS
G
,
,
,
′
′
=
 
Here, INTRANS performs the intensity or gray level 
transformations and G computes a contrast stretching 
transformation using the following MATLAB expression: 
(
)
(
)
(
)E
eps
F
M
Contrast
.^
/
.
1
/
.
1
+
+
=
 
where, parameter M must be in range [0,1]. The default 
value for M is 
(
)
(
)
F
double
im
mean
2
2
 and the default value for 
E is 4. Here, F is gray-level image and M is such result which 
is found by applying image double and median filtering 
operation on F. eps returns the distance from 1.0 to the next 
largest double-precision number, i.e. 
(
)
52
^
2 −
=
eps
. 
3) 
 Noise Reduction 
Noise reduction is a process of removing noise from a 
captured image. To remove noise some filtering techniques [1] 
can be proposed as follows: 
One method to remove noise is by convolving the original 
image with a mask that represent a low-pass filter or smoothing 
operation. For example, the Gaussian mask comprises elements 
determined by a Gaussian function. This convolution brings the 
value of each pixel into closer harmony with the values of its 
neighbors. In general, a smoothing filter sets each pixel to the 
average value, or a weighted average, of itself and its nearby 
neighbors; the Gaussian filter is just one possible set of 
weights. But smoothing filters tend to blur an image, because 
pixel intensity values that are significantly higher or lower than 
the surrounding neighborhood would "smear" across the area. 
Because of this blurring, linear filters are seldom used in 
practice for noise reduction.  
For the above reason, we proposed to use a non-linear filter 
which is called median filter. It is very good at preserving 
image detail if it is designed properly. To run a median filter: 
a) Consider each pixel in the image 
b) Sort neighboring pixels into order based upon their 
intensities 
c) Replace the original value of the pixel with the median 
value from the list 
A median filter is a rank-selection (RS) filter, a particularly 
harsh member of the family of rank-conditioned rank-selection 
(RCRS) filters [2]; a much milder member of that family, for 
example one that selects the closest of the neighboring values 
when a pixel's value is extremely in its neighborhood, and 
(IJCSIS) International Journal of Computer Science and Information Security, Vol. 1, No. 1, May 2009 
 
25
leaves it unchanged otherwise, is sometimes preferred, 
especially in photographic applications. 
Median filter technique is good at removing salt and pepper 
noise from an image, and also causes relatively little blurring of 
edges, and hence is often used in computer vision applications. 
4) 
 Edge Detection 
An edge may be regarded as a boundary between two 
dissimilar regions in an image. These may be different surfaces 
of the object, or perhaps a boundary between light and shadow 
falling on a single surface. In principle, an edge is easy to find 
since differences in pixel values between regions are relatively 
easy to calculate by considering gradients. Many edge 
extraction techniques [3] can be broken up into two distinct 
phases: 
 
• Finding pixels in the image where edges are likely to 
occur by looking for discontinuities in gradients. 
• Linking these edge points in some way to produce 
descriptions of edges in terms of lines, curves etc. 
For the proposed method, we detect edge using sobel edge 
detection method [6] upon the resulting image. Actually there 
are many kinds of edge detectors. We use first derivative edge 
detector (sobel) to detect edges of the image. Because, it’s 
calculation is very simple and fast to detect edges. On the other 
hand, if we use second derivative edge detector operator such 
as laplacian of gaussian operator then we will not be able to 
find the orientation of the edge because of using the laplacian 
filter. Again, if we use other kinds of gaussian edge detectors 
such as canny, shen castan, boie-cox operators then the 
operation is more complex [7]. 
C. Applying the Proposed Defect Detection Process 
All preprocessing operations are applied to the reference 
image, stored in the computer database to compare with the test 
image. Let, the resulting image is I2. Now we consider I1 as the 
resulting image found from the test image after applying all 
preprocessing operations. We propose here a new technique. 
We store I1 and I2 as matrix form to a file. Let, these two 
matrices are named as m1 and m2. Then we count the total 
number of black pixels (in binary, it is represented as 1) in m1 
and that in m2. These two are then compared. If the number of 
black pixels in m1 is greater than the number of black pixels in 
m2 then we can make decision that defect is found in the test 
image, otherwise we can say that no defect is present to the test 
image. To understand this concept clearly, consider the 
following example: 
Let, we have a test image and a reference image of equal 
size
)
5
5
( ×
. Now applying preprocessing steps on the test image 
we find matrix m1 whose value is: 
⎥
⎥
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎢
⎢
⎣
⎡
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
 
Again, applying the preprocessing operations on the 
reference image another matrix m2 is found: 
⎥
⎥
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎢
⎢
⎣
⎡
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
 
Here, the number of black pixels for the reference image is 
2 and for the test image this number is 6. So, here obviously 
6>2 and we can make decision that defect is found on the test 
image. 
The detailed block diagram of the proposed defect detection 
step is shown in the following Fig.  2. 
 
 
 
 
 
 
 
 
 
 
 
 
Figure  2.  Block Diagram of Defect Detection Part 
D.  Classifying the Defect Using All Proposed Algorithms                        
In the following, our proposed detailed algorithms to 
classify total six kinds of defects are given step by step:   
1) 
 Initial Steps before Classification 
a)   Plane Tiles 
Step1. After finding the binary image, apply morphological 
operation on it. 
Step 2. Now check every pixel elements of resulting image. 
Step 3. If any pixel element has value 1 then  
 
 
Change its value to 2. 
Step 4. Change such coordinates of binary image as 2 
which of the resulting image have value 2. 
Step 5. Finally, save this resulting matrix into a text file.    
b)  Printed Tiles 
Step 1. Check the reference image after processing and if 
any of its coordinates has value 1 then save these coordinates.   
Step 2. After finding the binary image from test image, 
apply morphological operation on it. 
Image after Edge  
Detection 
Counting the Number of 
Defected Pixels of Test 
Image, n1 
Counting the Number of 
Defected Pixels of 
Reference Image, n2 
(n1 > n2)? 
Defect Found
 
Yes
No
Defect Not Found
(IJCSIS) International Journal of Computer Science and Information Security, Vol. 1, No. 1, May 2009 
 
26
Step 3. Now check every pixel elements of this resulting 
image. 
Step 4. If any pixel element has value 1 then  
 
 
Change its value to 2. 
Step 5. Change such coordinates of binary test image as 2 
which of the resulting image have value 2. 
Step 6. Convert the previous saved coordinate values of 
binary test image as 0.   
Step 7. Finally, save this resulting matrix into a text file.    
 
2) 
 Algorithm to Determine Pinhole Defects 
Let, p_count as a variable for pinhole count, c_range as the 
range of corner, e_range as the range of edge and row as the 
maximum number of image pixels along any row and col as the 
maximum number of image pixels along any column. 
Step 1. Set,  temp_a =c_range ,    and   temp_b=e_range  
Step 2. Divide the total searching area for pinhole into three 
regions. 
Step 3. For left side region, 
 
for row consider the range from temp_a+1 to row-
c_range-1 
 
    for column consider the range from temp_b+1 to 
c_range  
 
    (a) check every pixel coordinates whether it is 0 or 
not.   
 
    (b) if it is true then  
 
 
     (i)  For each coordinate (i,j) check all of 
its eight neighbors.   
 
 
     (ii) If(i,j-1), (i,j+1), (i-1,j), (i+1,j) position 
values are 1 and the rest are 0, then 
 
 
           p_count will be incremented by 1. 
Step 4. For right side region, range for row is from 
temp_a+1 to row-c_range-1 and range for column is from col-
temp_a+1 to col-e_range. The rests are same as step-3. 
Step 5. For other middle side elements, range for row is 
from temp_b+1 to row-e_range and range for column is from 
col-temp_a+1 to col-c_range. The rests are same as step-3. 
Step 6. Finally, check value of p_count. If p_count>0, then 
pinhole is found, otherwise not found. 
 
3) 
 Algorithm to Determine Crack Defects 
 
Let, c_length as the range of crack. 
Step 1. Check every pixel coordinate (i,j) from left to right 
up to the last pixel element. 
Step 2. If any (i,j) has value 1 then 
 
(a) Consider its adjacent eight pixels and find which 
are 1. 
 
(b) If any adjacent pixel has value 1 then 
 
 
Current pixel coordinate will be updated to 
it. 
 
(c) Apply the backtracking process to find out all 
connected pixels and count the length. 
Step 3. Apply step 2 to all pixels and for each pixel find out 
the length of connected pixels. 
Step 4. Counting all length of the connected pixels found 
from step 2 and step 3, find out the maximum number and set it 
to c_count. 
Step 5. Finally, apply step 2 to specify the crack defected 
pixel coordinates so that other types of defects are not affected 
to it. 
Step 6. If c_count > c_length, then make decision that 
crack is found, otherwise crack is not found. 
 
4) 
 Algorithm to Determine Blob Defects 
Let, matx as size of blob, row as the maximum number of 
image pixels along any row and col as the maximum number of 
image pixels along any column. 
Step 1. Let, start=(matx/2)+1; Here start is the middle 
element of (matx*matx) .  
Step 2. Check every pixel coordinate (i,j) from left to right 
up to the last pixel element. 
 
for row consider the range from start to row-start+1 
 
for column consider the range from start to col-start+1  
 
(a)  If any pixel coordinate (i,j) is 2, then 
(i)  Considering it as the middle element and check the total 
(matx*matx) elements around it to find out how many 2 exists 
into these region. 
 
 
(ii)  Let, the total number of 2 is equal to 
b_length. 
 
 
(iii) If b_length = (matx*matx), then 
 
 
      Make decision that blob defect is found 
and exit from loop. 
 
 
 
(b) Otherwise, switch to next pixel coordinate at step 
2.  
Step 3. After searching every pixel coordinate, if there is no 
b_length matches to (matx*matx), then make decision that blob 
defect is not found.  
5) 
 Algorithm to Determine Spot Defects 
Let, matx as size of spot, row as the maximum number of 
image pixels along any row and col as the maximum number of 
image pixels along any column. 
Step 1. Let, start=(matx/2)+1; Here start is the middle 
element of (matx*matx) . 
(IJCSIS) International Journal of Computer Science and Information Security, Vol. 1, No. 1, May 2009 
 
27
Step 2. Check every pixel coordinate (i,j) from left to right 
up to the last pixel element. 
 
for row consider the range from start to row-start+1 
 
for column consider the range from start to col-start+1  
 
(a)  If any pixel coordinate (i,j) is 2, then 
(i)  Considering it as the middle element and check the total 
(matx*matx) elements around it to find out how many 2 exists 
into these region. 
 
 
(ii)  Let, the total number of 2 is equal to 
s_length. 
 
 
(iii) If s_length = (matx*matx), then 
 
 
      Make decision that spot defect is found 
and exit from loop. 
 
 
 
(b) Otherwise, switch to next pixel coordinate at step 
2.  
Step 3. After searching every pixel coordinate, if there is no 
s_length matches to (matx*matx), then make decision that spot 
defect is not found. 
 
6) 
 Algorithm to Determine Edge Defects 
Let, c_range as the range of corner, row as the maximum 
number of image pixels along any row and col as the maximum 
number of image pixels along any column.  
Step 1. Initially, take a variable e_count and set its value to 
0. 
Step 2. Consider four regions in up, down, left and right 
side. 
Step 3. For upper edge, 
 
row has fixed value 1 
 
      for column consider the range from c_range + 1 to 
col-c_range + 1 
 
      Consider each pixel coordinate (i,j). 
 
      (i) If (i,j) coordinate has value 1 or 2, then  
 
 
 
 
    Increment the value of e_count by 1 and 
go to step 7.  
 
      (ii) Otherwise, continue. 
Step 4. For lower edge, row has value row and range for 
column is from c_range + 1 to col-c_range + 1. The rests are 
same as step-3. 
Step 5. For left edge, column has value 1 and range for row 
is from c_range + 1 to row-c_range + 1. The rests are same as 
step-3. 
Step 6. For right edge, column has value col and range for 
row is from c_range + 1 to row-c_range + 1. The rests are same 
as step-3. 
Step 7. If e_count > 0, then make decision that edge defect 
is found. 
 
Otherwise, edge defect is not found.  
 
7) 
 Algorithm to Determine Corner Defects 
Let, row as the maximum number of image pixels along 
any row and col as the maximum number of image pixels along 
any column. 
Step 1. Initially, take a variable c_count and set its value to 
0. 
Step  2. Check every pixel coordinates (i,j) along the range 
for four corner elements. 
 
 
If any coordinate has value 2, then  
 
 
          Increment the value of c_count by 1.  
Step 3. If c_count is equal to the total corner area, then 
 
 
Make decision that corner defect is found. 
 
Otherwise, corner defect is not found. 
IV. EXPERIMENTAL RESULTS AND DISCUSSION 
A. 
 Defect Detection 
The proposed system detects defect successfully. In this 
section, we show the result of step by step process of the 
proposed defect detection method. The defect detection rate 
and time efficiency are compared with the existing method [3]. 
We also classify here different types of defects found through 
defect detection process. Here it is needed to mention that 
during the production, many numbers of tiles are produced in 
industries at the same time of same colors, shape and pattern. 
So, all the tiles of one shape are compared with that particular 
type of standard tile when processing through the computers.  
To understand our proposed defect detection process, we 
apply the proposed method on a sample RGB image for plane 
one colored tiles. Then we check if any kind of defect exists in 
this test image or not. For this, we apply our proposed 
preprocessing operations on this image such as image 
enhancement, noise reduction and edge detection. This is 
shown in the following Fig.  3. In this Fig. , we also show the 
reference RGB image for that test image and the output after 
applying preprocessing operations on it.  
 
 
 
 
 
 
 
(IJCSIS) International Journal of Computer Science and Information Security, Vol. 1, No. 1, May 2009 
 
28
      
 
              (a) Test Image                  (b) Gray Level Image 
      
 
     (c) Image after                       (d) Image after 
     Contrast Stretching                 Edge Detection  
        
 
  (e) Reference Image          (f) Image after Preprocessing  
Fig.  3: Proposed Preprocessing Steps Applied on Test Image and 
Reference Image 
Now consider the Fig.  3(d) and Fig. 3(f). The image of Fig.  
3(d) is found from the test RGB image after applying all the 
proposed preprocessing operations onto it. Then the total 
number of defected pixels is count in this image. Here the total 
number of defected pixels is 348. Again, the image of Fig.  3(f) 
is found from the reference RGB image after applying all 
previous operations onto it. In this image the total number of 
defected pixels is 105. According to our proposed defect 
detection method we can say, n1=348 and n2=105. As n1 > n2, 
so we can make decision that defect is found in the test image.  
Again, we apply the proposed defect detection method on a 
sample test RGB image for printed tiles. Like before, we check 
if any kind of defect exists in this test image or not. Then we 
apply our proposed preprocessing operations on this image. 
This is shown in the following Fig.  4. In this Fig. , we also 
show the reference RGB image for that test image and the 
output after applying preprocessing operations on it.  
      
 
       (a) Reference Image        (b) Final Image 
 
       
 
   (c) Test Image                   (d) Final Image 
Fig.  4: (a) Reference RGB Image, (b) Final Image after 
Preprocessing for Reference Image, (c) Test RGB Image, 
(d) Final Image after Preprocessing for Test Image 
 
Consider the Fig.  4(b) and Fig.  4(d). The image of Fig.  
4(b) is found from the test RGB image after applying all the 
proposed preprocessing operations onto it. Then the total 
number of defected pixels is count in this image. Here the total 
number of defected pixels is 982. Again, the image of Fig.  4(d) 
is found from the reference RGB image after applying all 
previous operations onto it. In this image the total number of 
defected pixels is 714. According to our proposed defect 
detection method we can say, n1=982 and n2=714. As n1 > n2, 
so we can make decision that defect is found in the test image.  
We have tested our proposed method for defect detection 
on about 50 ceramic tile images. In this case, the proposed 
defect detection efficiency is compared to the existing method 
[3]. We see that the detection rate for the proposed method is 
better than that of the existing method. Following Table II 
shows the efficiency comparison between the existing work 
and the proposed work and Fig. 5 represents the detection 
efficiency through a chart. 
 
TABLE II.  EFFICIENCY COMPARISON BETWEEN EXISTING WORK AND 
OUR WORK 
Detection Efficiency 
Number 
of Tiles 
Existing 
Work 
Our 
Work 
10 
90% 
100% 
20 
85% 
90% 
30 
86.67% 
90% 
40 
87.5% 
92.5% 
50 
88% 
92% 
Average 
87.4% 
93% 
 
(IJCSIS) International Journal of Computer Science and Information Security, Vol. 1, No. 1, May 2009 
 
29
Defect Detection Efficiency
80
85
90
95
100
105
0
20
40
60
Number of Tiles
Detection RateE x is ting
Work
Our Work
 
Fig. 5: Efficiency Comparison Chart between Existing Work and Our 
Work 
We also compute the required time for the proposed method 
and the existing method [3]. The proposed method needs less 
time than the existing one. Table III shows the time comparison 
between the existing work and proposed work. Fig. 6 
represents time comparison through a chart.   
 
TABLE III.  TIME COMPARISON BETWEEN EXISTING WORK AND OUR 
WORK 
Required Time (in sec.) 
Number 
of Tiles 
For 
Existing 
Method 
For 
Our 
Method 
10 
38.6363 
10.3023 
20 
77.4986 
20.4579 
30 
116.941 
30.5645 
40 
157.204 
40.2381 
50 
193.887 
49.8988 
 
Time Comparison
0
50
100
150
200
250
10
20
30
40
50
Number of Tiles
Time in SecExisting
Method
Proposed
Method
Fig.  6: Time Comparison Chart between Existing Work and Our Work 
B. 
 Defect Classification 
We need to classify the various kinds of defects after defect 
detection. For this purpose we store the output of the above 
resulting image into a file as matrix form. Then previously 
mentioned algorithms are applied on that matrix. In the 
following Table IV, we show our result after applying the 
proposed classification algorithms for both plane and printed 
tiles mentioned above.  
 
TABLE  IV.  CLASSIFICATION RESULT 
Types of 
Defect 
Result (for 
Plane Tiles) 
Result (for 
Printed Tiles) 
Pinhole 
Found 
Not Found 
Crack 
Not Found 
Found 
Blob 
Found 
Found 
Spot 
Not Found 
Not Found 
Edge 
Not Found 
Not Found 
Corner 
Not Found 
Not Found 
 
Table V represents the classification efficiency of the 
proposed method for both plane and printed tiles and Fig.  7 
represents this efficiency through a chart.   
 
TABLE V.  CLASSIFICATION EFFICIENCY OF THE PROPOSED METHOD FOR 
100 TILES 
Name of 
Defects 
Classification Rate 
for Both Plane and 
Printed Tiles (%) 
Pinhole 
93.48 
Crack 
86.49 
Blob 
87.50 
Spot 
90.00 
Edge 
96.77 
Corner 
93.55 
 
Fig.  7: Classification Efficiency Chart for Proposed Method 
 
In this section, we have shown the result of the proposed defect 
detection method applied on a particular RGB image. We also 
have show the comparison between the existing method [3] and 
the proposed method in the case of detection efficiency and 
time efficiency. As a result, we find that our proposed method 
is better than the existing one. The detection rate of the 
proposed method is average 93% for a number of tiles, where 
for the existing method this rate is 87.4%. Again, the proposed 
method requires total 49.8988 seconds to process 50 tiles, 
where the existing method requires a huge time and it is total 
(IJCSIS) International Journal of Computer Science and Information Security, Vol. 1, No. 1, May 2009 
 
30
193.887 seconds. We also have shown the classification 
efficiency for different types of defects. 
 
V. 
 CONCLUSION AND FUTURE WORK 
 
We have proposed a defect detection method for ceramic 
tiles and compared our technique with the existing defect 
detection method. We also have shown a comparison for defect 
detection and processing time between the proposed method 
and the existing method [3]. Detection rate of the proposed 
method is better than that of the existing method and we need 
less time to detect defects than the existing one. We also have 
established defect classification algorithms for different types 
of defects. Finally, we have calculated the performance of 
efficiency for defect classification.   
The proposed method fails to detect the glaze and scratch 
faults. So it may be future work to detect and classify the glaze 
and scratch faults. We propose no method to improve the 
computational time for the proposed classification technique. In 
this case, a future work should be done on reducing the total 
computational time for defect classification.  
REFERENCES 
 
[1] R. C. Gonzalez, R. E. Woods, “Digital Image Processing”, Pearson 
Education (Singapore), Pte. Ltd., Indian Branch, 482 F.I.E. Patparganj, 
2005-2006. 
[2] Puyin Liu, Hongxing Li, “Fuzzy Neural Network Theory and 
Application”. World Scientific, 2004. 
[3] H. Elbehiery, A. Hefnawy, and M. Elewa, “Surface Defects Detection 
for Ceramic Tiles Using Image Processing and Morphological 
Techniques”, Proceedings of World Academy of Science, Engineering 
and Technology, vol 5, pp 158-160, April 2005, ISSN 1307-6884. 
[4] C. Boukouvalas, J. Kittler, R. Marik, M. Mirmehdiand, M. Petrou, 
“Ceramic Tile Inspection for Colour and Structural Defects”, under 
BRITE-EURAM, project no. BE5638, pp 6, University of Surrey, 2006. 
[5] Se Ho Choi, Jong Pil Yun, Boyeul Seo, Young Su Park, Sang Woo Kim, 
“Real-Time Defects Detection Algorithm for High-Speed Steel Bar in 
Coil”, Proceedings of World Academy of Science, Engineering and 
Technology, Volume 21, January 2007, ISSN 1307-6884. 
[6] Se Ho Choi, Jong Pil Yun, Boyeul Seo, Young Su Park, Sang Woo Kim, 
“Real-Time Defects Detection Algorithm for High-Speed Steel Bar in 
Coil”, Proceedings of World Academy of Science, Engineering and 
Technology, Volume 21, January 2007, ISSN 1307-6884. 
[7] Mohamed Roushdi, “Comparative Study of Edge Detection Algorithms 
Applying on the Grayscale Noisy Image Using Morphological Filter”, 
GVIP Journal, Volume 6, Issue 4, December, 2006. 
 
 
AUTHORS PROFILE 
 G.M. Atiqur Rahaman received B.Sc. in Computer Science and 
Engineering with Distinction from Computer Science and Engineering 
Discipline in 2003 from Khulna University, Bangladesh. Currently he is 
Assistant Professor of the same Discipline of the same University. He has 
published about 08 papers in national and international journals as well as 
international conference proceedings. His areas of interest include Machine 
Intelligence, Data Mining, Computer Vision, Digital Image Processing, Color 
Informatics etc. 
 
 
 
`
20
40
60
80
100
C ra
ck
P in
hol
e
Blo
b
S p
ot
Ed
g e
C o
rne
r
Type of Defect
Number of Tiles
(IJCSIS) International Journal of Computer Science and Information Security, Vol. 1 No.1 May 2009
 
 
 
High Transmission Bit Rate of A thermal Arrayed Waveguide Grating (AWG) 
Module in Passive Optical Networks 
 
Abd El–Naser A. Mohammed1, Ahmed Nabih Zaki Rashed2*,  
Gaber E. S. M. El-Abyad3  and Abd El–Fattah A. Saad4 
  
 
1,2,3,4Electronics and Electrical Communication Engineering Department 
Faculty of Electronic Engineering, Menouf 32951, Menoufia University, EGYPT 
1E-mail: abd_elnaser6@yahoo.com, 2*E-mail: ahmed_733@yahoo.com 
 
Tel.: +2 048-3660-617, Fax: +2 048-3660-617 
 
 
Abstract―In the present paper, high transmission bit 
rate of a thermal arrayed waveguide grating (AWG) 
which 
is 
composed 
of 
lithium 
niobate 
(LiNbO3)/polymethyl metha acrylate (PMMA) hybrid 
materials on a silicon substrate in Passive Optical 
Networks (PONs) has parametrically analyzed and 
investigated over wide range of the affecting parameters. 
We have theoretically investigated the temperature 
dependent wavelength shift of the arrayed waveguide 
grating (AWG) depends on the refractive-indices of the 
materials and the size of the waveguide. A thermalization 
of the AWG can be realized by selecting proper values of 
the material and structural parameters of the device. 
Moreover, we have analyzed the data transmission bit 
rate of a thermal AWG in passsive optical networks 
(PONs) based on Maximum Time Division Multiplexing 
(MTDM) technique.  
 
        Keywords−PONs; 
Arrayed 
waveguide 
gratings 
(AWGs); integrated optics; optical planar waveguide; 
optical fiber communications; MTDM technique. 
 
 
I. INTRODUCTION 
 
        With the explosive growth of end user demand for 
higher bandwidth, various types of passive optical networks 
(PONs) have been proposed. PON can be roughly divided 
into two categories such as time-division-multiplexing 
(TDM) and ultra wide wavelength-division-multiplexing 
(UW-WDM) methods [1]. Compared with TDM-PONs, 
WDM-PON systems allocate a     separate wavelength to 
each subscriber, enabling 
the delivery of dedicated 
bandwidth per optical network unit (ONU). Moreover, this 
virtual point-to-point connection enables a large guaranteed 
bandwidth, protocol transparency, high quality of service, 
excellent 
security, 
bit-rate 
independence, 
and 
easy 
upgradeability. Especially, recent good progress on athermal 
arrayed waveguide grating (AWG) and cost-effective 
colorless ONUs [2] has empowered WDM-PON as an 
optimum solution for the access network. However, fiber link 
failure from the optical line terminal (OLT) to the ONU leads 
to the enormous loss of data. Thus, fault monitoring and 
network protection are crucial issues in network operators for 
reliable network. To date [3], many methods have been 
proposed 
for 
network 
protection. 
In 
the 
ITU-T 
recommendation on PONs (G.983.1) duplicated network 
resources such as fiber links or ONUs are required. The 
periodic and cyclic properties of AWGs are used to 
interconnect two adjacent ONUs by a piece of fiber. In the 
recent years, arrayed waveguide gratings (AWGs) have 
appeared to be one of attractive candidates for high channel 
count Mux/DeMux devices to process optical signals in a 
parallel manner. Its low chromatic dispersion [4], typically 
±5 ps/nm — ±10 ps/nm, makes it possibly be used for 40 
Gbit/s 
systems. However, 
it 
is well known 
that 
manufacturing AWGs involves a series of complex 
production processes and requires bulky facilities [5]. Their 
cost remains a big issue. Further, the technical complexity 
leads to low yield and poor performance. The former, no 
doubt, further increases the production cost while the latter 
degrades the signal quality and system’s performance [6], 
exhibiting high insertion loss, high channel crosstalk, low 
channel uniformity, and high polarization dependent loss. 
More vitally, AWGs require active temperature control in 
order to stabilize the thermal wavelength drift and 
temperature-dependent loss variations [7]. Due to its 
capability to increase the aggregate transmission capacity of 
a single-strand optical fiber, the arrayed waveguide grating 
(AWG) multiplexer is considered a key component in the 
construction of a dense wavelength-division-multiplexing 
system [8]. However, an AWG made of silica is so sensitive 
to the ambient temperature that the output wavelength 
changes by as much as 0.66 nm/ºC [9]. In the present study, a 
hybrid material waveguide with lithium niobate (LiNbO3) 
core material and PMMA cladding material is considered as 
the most attractive a thermal structure because of its 
resistance to the thermo-optic sensitivity of the materials. 
First, 
the principle of 
the a 
thermal AWG with 
LiNbO3/PMMA hybrid materials is described, and the 
relative formulas are derived for analyzing the temperature 
dependence of the AWG. Second, the theoretical analysis of 
the data transmission bit rate of a thermal AWG in PONs 
based on MTDM technique . Finally, a conclusion is reached 
based on the analysis and general discussion. 
 
 
Manuscript received  April 17, 2009
 
Manuscript revised  , May 2009
 
13
(IJCSIS) International Journal of Computer Science and Information Security, Vol. 1 No.1 May 2009
 
 
 
II. A THERMAL AWG MODULE IN PONS ARCHITECTURE MODEL 
       
 
 
 
 
 
 
 
 
 
 
Fig. 1. Simplified Passive Optical network architecture model. 
 
       The network architecture is shown in Fig. 1. It is based 
on two cascaded Athermal arrayed waveguide gratings 
(AWGs). The first stage is an Nx1a thermal AWG located 
at the optical line terminal (OLT) or central office (CO). 
The functionality of this a thermal AWG is to route optical 
signals generated by the OLT laser diodes stack to each of 
the network branches to which the OLT will serve [4]. The 
second stage is a 1× M a thermal AWG located at the 
remote node. Its task is to demultiplex the M incoming 
wavelengths to each of the output ports, which connect to 
optical network channels and then to the number of 
supported users. The entire network routing intelligence is 
located at the CO in order to provide easy upgradeability 
and easy integration with the backbone. The two cascade a 
thermal AWGs are connected to each other by the single 
mode optical fiber cables [5].  
 
III. Features Of A Thermal Arrayed 
Waveguide Grating Module 
 
        Arrayed waveguide grating (AWG) which handles the 
function of wavelength multiplexer/demultiplexer 
is 
extensively used in configuring optical communication 
networks that are becoming more diversified. Since the 
transmission wavelength of an AWG is temperature 
dependent, it was a common practice to control its 
temperature using heaters or Peltier elements. The AWG 
consists of input waveguides, arrayed waveguide, slab 
waveguide and output waveguides, constituting a diffraction  
 
grating that takes advantage of the optical path difference in 
the arrayed waveguide. Figure 2 shows a schematic view of 
AWG circuitry. As ambient temperature changes, the phase 
front at each wavelength generated by the arrayed 
waveguide will tilt due to the change in the refractive index 
of the optical waveguide and the linear expansion of the 
silicon substrate, causing a shift of the focusing point on the 
output waveguide within the slab waveguide [10].  
 
  
Fig. 2. Sechamtic view of a thermal AWG. 
  
 
As shown in Fig. 3, the thermal arrayed waveguide grating 
(AWG) with cross-sections is designed as square shape with 
the core width a, of lithium niobate (LiNbO3) material and 
PMMA polymer overcladding and undercladding material 
on a silicon substrate. 
OLT
 
       Single mode fiber link
 
A thermal 
AWG 1xM
A thermal 
AWG 1xM
 
 
 
Laser 
Diodes 
 
Supported 
Number of 
Users 
 
Supported 
Number of 
Users 
 
A thermal 
AWG 
N X 1 
Optical 
Network 
Channels
Optical 
Network 
Channels
Central 
Office (CO) 
14
(IJCSIS) International Journal of Computer Science and Information Security, Vol. 1 No.1 May 2009
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Fig. 3.  A structure view of cross-section and refractive- index profile of 
hybrid materials LiNbO3/PMMA. 
 
IV. REFRACTIVE-INDEX OF HYBRID 
MATERIALS 
 
IV. 1.  Lithium Niobate (LiNbO3) Core Material 
 
        The investigation of both the thermal and spectral 
variations of the waveguide refractive index (n) require 
Sellmeier equation. The set of parameters required to 
completely characterize the temperature dependence of the 
refractive-index (n1) is given below, Sellmeier equation is 
under the form [11]:  
(
)
2
10
2
9
2
8
7
2
6
5
2
4
3
2
1
2
1
λ
λ
λ
A
A
H
A
A
H
A
A
H
A
A
H
A
A
n
−
−
+
+
+
−
+
+
+
=
 
 
 
 
 
 
(1)                                       
where λ is the optical wavelength in μm and
2
0
2 T
T
H
−
=
. T 
is the temperature of the material, C, and T0 is the reference 
temperature and is considered as 27 C. The set of 
parameters of Sellmeier equation coefficients, LiNbO3, are 
recast and dimensionally adjusted as below [11]:  
A1=5.35583, A2=4.629 x 10-7, A3=0.100473,   A4=3.862 x 
10-8, A5=0.20692, A6= -0.89 x 10-8,   A7=100, A8=2.657 x 
10-5, A9=11.34927, and A10=0.01533. 
Equation (1) can be simplified as the following expression: 
2
10
2
9
2
78
2
56
2
34
12
2
1
λ
λ
λ
A
A
A
A
A
A
n
−
−
+
−
+
=
       
(2) 
where: A12=A1+A2H,  
  A34=A3+A4H,  A56=A5+A6H, 
and    A78=A7+A8H. 
Then, the differentiation of Eq. (2) w. r. t λ which gives: 
(
)
(
)
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
+
−
+
−
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛ −
=
10
2
2
9
2
78
2
2
56
2
34
1
1
A
A
A
A
A
n
d
dn
λ
λ
λ
λ
  
(3) 
In the same way, the second differentiation w. r. t λ yields: 
(
)
[
]
(
)
(
)
[
]
(
)
⎥
⎥
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎢
⎢
⎣
⎡
+
−
−
−
+
−
−
−
−
=
10
3
2
9
2
2
2
9
2
78
3
2
56
2
2
2
56
2
34
1
2
1
2
4
4
1
A
A
A
A
A
A
A
n
d
n
d
λ
λ
λ
λ
λ
λ
λ
 
 
(4) 
Also, the differentiation w. r. t T gives: 
(
)
(
)
(
)
⎥
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎢
⎣
⎡
−
+
−
+
−
+
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
2
9
2
8
2
2
56
2
34
56
6
4
2
56
2
2
1
1
2
A
A
A
A
A
A
A
A
A
n
T
dT
dn
λ
λ
λ
     
(5) 
 
IV. 2. PMMA Polymer Cladding Material 
 
        The Sellmeier equation of the refractive-index is 
expressed as the following [12]: 
2
6
2
2
5
2
4
2
2
3
2
2
2
2
1
2
2
1
C
C
C
C
C
C
n
−
+
−
+
−
+
=
λ
λ
λ
λ
λ
λ
    
 
(6) 
The parameters of Sellmeier equation coefficients, PMMA, 
as a function of temperature [12]: C1=0.4963, C2=0.07180 
(T/T0), C3=0.6965, C4=0.1174 (T/T0), C5=0.3223, and 
C6=9.237. 
Then the differentiation of Eq. (6) w. r. t T yields: 
(
)
(
)
(
) ⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
−
+
−
=
2
2
4
2
4
3
2
2
2
2
2
1
0
2
2
2
635
.
1
0718
.
0
C
C
C
C
C
C
T
n
dT
dn
λ
λ
λ
  
(7) 
    
V. THEORETICAL MODEL ANALYSIS 
 
V. 1. Model of A thermal Arrayed Waveguide 
Grating (AWG) 
 
       We present the a thermal condition and the relative 
formulas of LiNbO3/PMMA hybrid materials AWG on a 
silicon substrate. The temperature dependence of AWG 
center wavelength is expressed as [13, 14]. 
⎟
⎠
⎞
⎜
⎝
⎛
+
=
sub
c
c
c
c
c
n
dT
dn
n
dT
d
α
λ
λ
 
         
 
 (8) 
where T is the ambient temperature, C, λc is the center 
wavelength of the arrayed waveguide grating, µm, nc is the 
effective refractive-index of the arrayed waveguide grating, 
αsub is the coefficient of thermal expansion of the Si 
substrate, and 
dT
dnc  is the thermo-optic (TO) coefficient of 
the waveguide. By integrating Eq. (8), we can obtain the 
following expression: 
  
(
)
T
c
c
sub
e
n
C
α
λ =
         
(9) 
where C is an integrating constant. Assume that λc=λ0, and 
nc=nc0 when T=T0 at room temperature, we can determine C 
as the following: 
 
(
)
0
0
0
T
c
sub
e
n
C
α
λ
−
=
      
 (10) 
Substituting from Eq. (10) into Eq. (9), we can obtain: 
Si Substrate 
LiNbO3 core n1
 
    PMMA overcladding  n2
a
    PMMA undercladding  n2
 
15
(IJCSIS) International Journal of Computer Science and Information Security, Vol. 1 No.1 May 2009
 
 
 
  
(
)
[
]
0
0
0
T
T
c
c
c
sub
e
n
n
−
=
α
λ
λ
      
(11) 
From Eq. (11) we obtain the central wavelength shift caused 
by 
the 
temperature 
variation 
as:   
(
)
(
)
[
]
co
T
T
c
c
c
n
e
n
n
sub
−
=
−
=
Δ
− 0
0
0
0
α
λ
λ
λ
λ
      
(12) 
Taking Δλ = 0, from Eq. (12) we can obtain the a thermal 
condition of the AWG as: 
  
(
)
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
−
0
0
ln
c
c
sub
n
n
T
T
α
    
(13)  
Then by differentiating Eq. (13), the a thermal condition of 
the AWG can also be expressed in another form as the 
following [14]: 
  
c
sub
c
n
dT
dn
α
−
=
     
 (14) 
The effective refractive index of the arrayed waveguide 
grating (AWG) is given by [15]: 
 
(
)
[
]
(
)
,
2
2
2
2
2
1
2
2
2
2
2
1
n
b
n
n
k
n
b
n
n
k
k
nc
+
−
=
+
−
=
=
β
  (15) 
where β is the propagation constant of the fundamental 
mode, k is the wave number,  and b is the normalized 
propagation constant and is given by [15]: 
  
(
)
,
9660
.
0
1428
.
1
2
⎟
⎠
⎞
⎜
⎝
⎛
−
=
V
V
b
     
(16) 
where V is the normalized frequency. For single mode step 
index optical fiber waveguide, the cut-off normalized is 
approximately V= Vc= 2.405, and by substituting in Eq. (16) 
we can get the normalized propagation constant b at the cut-
off normalized frequency approximately b ≈ 0.5, and then by 
substituting in Eq. (15) we can obtain: 
  
(
)
,
2
1
2
2
2
1
n
n
nc
+
=
     
(17) 
By taking the square root of Eq. (17) yields: 
  
(
)
,
7
.
0
2
1
2
2
2
1
n
n
nc
+
=
    
 (18) 
The cut-off normalized frequency for single mode step index 
optical fiber waveguide is given by the following expression 
[15]: 
  
(
)
,
2
2
1
2
2
2
1
n
n
a
V
off
cut
c
−
=
−
λ
π
      
(19) 
Assume that the cut-off wavelength is equal to the central 
wavelength to transfer the fundamental modes only, that is 
λcut-off = λc. Eq. (19) can be expressed in another form as 
follows:   
(
)
,
405
.
2
4
.
1
2
1
4
2
4
1
c
c
n
n
n
a
−
=
π
λ
     
(20) 
Equation (20) can be simplified as follows: 
  
(
)
,
83
.
1
2
1
4
2
4
1
c
c
n
n
n
a
−
=
λ
    
 (21) 
Equation (21) can be expressed in another form as follows: 
  
(
)
,
35
.
3
2
4
2
4
1
2
c
c
n
n
a
n
λ
−
=
   
 (22) 
By substituting from Eq. (22) into Eq. (14) yields: 
  
(
)
.
35
.
3
2
4
2
4
1
2
c
sub
c
n
n
a
dT
dn
λ
α
−
−
=
  
 (23) 
The effective refractive index nc is dependent on the 
refractive indices of the materials and on the size and shape 
of the waveguide, then by selecting proper materials and 
structural parameters of the waveguide to satisfy Eq. (23), 
an a thermal arrayed waveguide grating (AWG) can be 
designed.  
 
V. 2. Theoretical Model Analysis of High Data 
Transmission Bit Rate 
 
        The total B.W is based on the total chromatic 
dispersion coefficient Dt [16], where: 
    Dt = Dm + Dw     
(24) 
where Dm is the material dispersion coefficient in sec/m2, 
and Dw is the waveguide dispersion coefficient in sec/m2. 
Both Dm, Dw are given by [17] (for the fundamental mode): 
 
,
2
1
2
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
=
λ
λ
d
n
d
C
Dm
  sec/m2    
(25) 
  
,
1
2
Y
n
n
C
n
Dw
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
Δ
−
=
λ
  sec/m2   
 (26) 
where C is the velocity of the light, 3 x108 m/sec, 1n is the 
core refractive-index, 
2n is the cladding refractive-index, Y 
is a function of wavelength, λ [17].  
The relative refractive-index difference Δn is defined as 
[17]: 
  
2
1
2
2
2
1
2n
n
n
n
−
=
Δ
               
(27) 
The total pulse broadening due to total chromatic dispersion 
coefficient Dt  is given by [17]: 
  
λ
τ
Δ
=
Δ
L
Dt
,  nsec   
(28) 
where Δλ is the spectral line-width of the optical source, nm, 
and L is the length of single-mode fiber waveguide, m.  
The maximum time division multiplexing (MTDM) 
transmission bit rate is given by [17]: 
  
τ
τ
Δ
=
Δ
=
25
.
0
4
1
rm
B
 , Gbit/sec   
(29) 
The optical signal wavelength span 1 μm ≤ λsi, optical 
signal wavelength≤ 1.65 μm is divided into intervals per 
link as follows: 
  
link
m
N
N
L
L
i
f
/
,
65
.
0
0
μ
λ
λ
λ
=
−
=
Δ
  
 
(30) 
Then the MTDM bit rates per 
fiber cable link is given 
by the following expression: 
  
link
Gbit
N
x
B
ch
rLink
sec/
/
,
25
.
0
τ
Δ
=
  
 
(31) 
where Nch is the number of optical network channels in the 
fiber cable link, and NL is the number of  links in the fiber 
cable core and is up to 24 links/core.  
 
 
16
(IJCSIS) International Journal of Computer Science and Information Security, Vol. 1 No.1 May 2009
 
 
 
 
 
 
 
 
 
-5
-4.5
-4
-3.5
-3
-2.5
-2
20
25
30
35
40
45
50
55
60
65
70
 
Temperature, T [C]
 
  
 
  
Fig. 4. Variation of thermo-optic (TO) coefficient versus temperature when n1=2.33, n2=1.52, a= 5 μm.
  
 
-0.016
-0.01
-0.004
0.002
0.008
0.014
0.02
20
25
30
35
40
45
50
55
60
65
70
n1 = 2.33
 = 2.32
 = 2.30
a thermal
  
 
Temperature, T [C]
  
 
 
Fig. 5. Variation of the central wavelength shift versus temperature for different core refractive-indices.
  
-0.016
-0.01
-0.004
0.002
0.008
0.014
0.02
20
25
30
35
40
45
50
55
60
65
70
n2 = 1.52
 = 1.51
 = 1.50
a thermal
 
Temperature, T [C]
 
 
Fig. 6. Variation of the central wavelength shift versus temperature for different cladding refractive-indices.
  
Thermo-optic coefficient dnC/dT [x10-6/ºC] Central wavelength shift Δλ [nm] Central wavelength shift Δλ [nm] 17
(IJCSIS) International Journal of Computer Science and Information Security, Vol. 1 No.1 May 2009
 
 
 
-0.016
-0.01
-0.004
0.002
0.008
0.014
0.02
20
25
30
35
40
45
50
55
60
65
70
a = 5 μm
 = 4.5 μm
 = 4 μm
a thermal
 
Temperature, T [C]
  
 
 
Fig. 7. Variation of the central wavelength shift versus temperature for different core width of  a thermal AWG.
  
 
-30
-25
-20
-15
-10
-5
1
1.04
1.08
1.12
1.16
1.2
1.24
1.28
1.32
1.36
1.4
1.44
1.48
1.52
1.56
1.6
1.64
∆n = 0.3
 = 0.4
 = 0.5
 
Optical signal wavelength, λ [µm]
  
 
Fig. 8. Total chromatic dispersion coefficient versus optical signal wavelength at the assumed set of parameters.
 
 
3
5
7
9
11
13
15
17
19
21
1
1.04
1.08
1.12
1.16
1.2
1.24
1.28
1.32
1.36
1.4
1.44
1.48
1.52
1.56
1.6
1.64
∆n = 0.3
 = 0.4
 = 0.5
 
Optical signal wavelength, λ [µm]
 
 
Fig. 9. MTDM transmission bit rate/channel versus optical signal wavelength a the assumed set of parameters.
  
 
 Central wavelength shift Δλ [nm] Total chromatic dispersion Dt [psec/nm.m]  MTDM bit rate/channel Brm [Gbit/sec] 18