Design of Unipolar (Optical) Orthogonal Codes & their Maximal Clique Sets

1. Design of Unipolar (Optical) Orthogonal
Codes and Their Maximal Clique Sets
by
Ram Chandra Singh Chauhan
(PhD/07/EC/539)
Under the Supervision of
Dr. Y. N. Singh Dr. R. Asthana
Professor Associate Professor
IIT, Kanpur HBTI, Kanpur
to
Faculty of Engineering & Technology
UPTU, Lucknow
July 11, 2015

2. CONTENTS
I. The Research Problem
II. Literature Survey
III. Objectives
IV. Methodology
V. Summary of Results
VI. Conclusions
VII. Future Directions
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3. Background of the Problem
 History of Communication among Humans
 Current demand in the field of communication
technology & research
 Limitations of current mediums
 Alternative medium as optical fiber
 Hybrid technology or scheme as Optical CDMA
 Design of optical CDMA unipolar codes
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4. Research Problem
 How to access optical fiber medium by multiple users
asynchronously ?
 Asynchronous CDMA scheme is better option to reduce
complexity of the system
 Asynchronous CDMA requires unipolar orthogonal
codes as signature sequences to multiple users
 How to find the multiple set of unipolar orthogonal
codes with maximum cardinality and orthogonality ?
 Search of an optimum solution
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5. Literature Survey
 Optical CDMA
 Types of Optical CDMA
– Incoherent Optical CDMA
• Temporal Spreading (1d)
• Spectral Amplitude Coding (1d)
• Spatial Coding (1d)
• Wavelength Hopping Time Spreading (2d)
• Wavelength Hopping Time Spreading Spatial Coding (3d)
– Coherent Optical CDMA
• Temporal Phase Coded
• Spectral Phase Coded
• Polarization Encoded
 Multiple Access Interference & Reduction
Schemes
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6. Literature Survey
One Dimensional Uni-polar (Optical)
Orthogonal Codes
– Conventional Representations
• Weighted Position Representation (WPR)
• Fixed Weighted Position Representation (FWPR)
– Calculations of Correlation Constraints
– Already Proposed 1-D OOC Design Schemes
in Literature
– Comparison with Ideal Scheme
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7. Literature Survey
 Two Dimensional Uni-polar (Optical)
Orthogonal Codes or Matrix Codes
– Conventional Representations
• Binary Matrix Representation (BMR)
• Weighted Positions Representation (WPR)
– Calculations of Correlation Constraints
– Already Proposed 2-D OOC Design Schemes in
Literature
– Comparison with Ideal Scheme
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8. Literature Survey
 Optical CDMA Network
OSC=Optical Star Network
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OSC -
1.1
OSC-
1.2
OSC-
1.3
OSC-
1.N
OSC-
2.1

9. Literature Survey
 Optical CDMA with Transmitter and Receiver
Section
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Source of
Binary
Information
Optical
Pulse
Genera
tor
Optical
Orthogo
nal
Encoder Optical
Star
Coupler
Optical
Hard
Limiter
Optical
Orthogo
nal
Decoder
Destination
for Binary
Information

10. Literature Survey
 Optical Orthogonal Encoder and Decoder for
code length n =7, weight w =3 with weighted positions at
(1,2,4)
OS=Optical Splitter
OC=Optical Combiner
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OS OC
OS OC

11. Objectives
 To Find a scheme or algorithm generating
multiple maximal clique sets of 1-D UOC
with maximum size
 To Find a scheme or algorithm generating
multiple maximal clique sets of 2-D UOC
with maximum size
 Comparison of these schemes with
hypothetical Ideal schemes
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12. One Dimensional Uni-polar (Optical)
Orthogonal Codes
Weighted Position Representation (WPR)
– Example: X = 1000100001000000100,
– Code length n=19, weight w=4
– WPR (X)= (0,4,9,16),(3,8,15,18), (2,7,14,17), (1,6,13,16),
(0,5,12,15), (4,11,14,18), (3,10,13,17), (2,9,12,16),
(1,8,11,15), (0,7,10,14), (6,9,13,18), (5,8,12,17),
(4,7,11,16), (3,6,10,15), (2,5,9,14), (1,4,8,13), (0,3,7,12),
(2,6,11,18), (1,5,10,17)
Fixed WPR
– FWPR (X)= [(0,4,9,16); (0,5,12,15); (0,7,10,14);
(0,3,7,12)]
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13. One Dimensional Uni-polar (Optical)
Orthogonal Codes
Difference of Positions Representation
(DoPR), proposed representation
– Example: X = 1000100001000000100,
n=19, w=4
– FWPR (X)= [(0,4,9,16); (0,5,12,15); (0,7,10,14);
(0,3,7,12)]
– DoPR (X)= (4,5,7,3),(5,7,3,4), (7,3,4,5), (3,4,5,7)
– Standard DoPR (X) = (3,4,5,7), unique representation
Extended DoPR , proposed representation
– EDoPR (X)= [(3,7,12); (4,9,16); (5,12,15);
(7,10,14)] ; FWPR (X)=EDoPR(0,X)
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14. One Dimensional Uni-polar (Optical)
Orthogonal Codes
Relationship Among Represenatation
– Example: standard DoPR(X) = (a,b,c,d),
n=19, w=4, such that, a+b+c+d=19,
– DoPR (X)= (a,b,c,d), (b,c,d,a), (c,d,a,b), (d,a,b,c)
– EDoPR (X)= [(a,a+b,a+b+c); (b,b+c,b+c+d);
(c,c+d,c+d+a); (d,d+a,d+a+b)]
– EDoPR(0,X)= FWPR (X)
– FWPR can be converted directly into an unique
binary sequence and their n-1 cyclically shifted
versions also
– All the codes for n=19, w=4 can be generated in
standard DoPR .
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15. One Dimensional Uni-polar (Optical)
Orthogonal Codes
Calculation of Correlation Constraints
– Auto-correlation Constraint of code X
• If X is a binary sequence
• If X is WPR(X)= XP
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1
0
0 1.
( )mod( ).
n
ax t t m
t
x x for m n
t m implies t m n




   
 

( ) ( ), (0 1)ax P PX a X a n      

16. One Dimensional Uni-polar (Optical)
Orthogonal Codes
Calculation of Correlation Constraints
– Auto-correlation Constraint of code X, proposed
• If X is a DoPR sequence,
• The maximum non-zero shift auto-correlation of the
uni-polar code is equal to one plus maximum number
of common DoP elements between two rows of EDoP
matrix of the code.
• where
• . are DoP elements of two rows of
EDoP matrix of the code X.
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1 1
1 1
1 (0 : 1), ( 1: 1)
w w
ax xij xkl
j l
e e for i w k i w
 
 
      
1
0
xij xkl
xij xkl
xij xkl
if e e
e e
if e e
 
 

&xij xkle e

17. One Dimensional Uni-polar (Optical)
Orthogonal Codes
Calculation of Correlation Constraints
– Cross-correlation Constraint of codes pair X,Y
• If X,Y are binary sequences
• If X,Y are WPR(X)= XP and WPR(Y)= YP
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1 1
0 0
, 0 1.
n n
cxy t t m t t m
t t
x y or y x for m n
 
 
 
    
( ) (a ), 0 1.cxy P PX Y a n      

18. One Dimensional Uni-polar (Optical)
Orthogonal Codes
Calculation of Correlation Constraints
– Cross-correlation Constraint of code X and Y,
(proposed)
• If X,Y are DoPR sequences,
 The cross-correlation of the uni-polar codes X and Y is equal
to one plus maximum common DoP elements between any
two rows of EDoP matrices of code X and code Y
respectively.
• where
• are DoP elements of rows of EDoP matrices
of code X and Y respectively .
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&xij ykle e
1 1
1 1
1 , (0: 1), (0: 1)
w w
cxy xij ykl
j l
e e for i w k w
 
 
     
1
0
xij ykl
xij ykl
xij ykl
if e e
e e
if e e
 
 


19. Design of Maximal Set of 1D
Uni-polar (Optical) Orthogonal Codes
 Algorithm One
– For code length ‘n’ and code weight ‘w’, all the
codes in standard DoPR are generated starting
from to with
enumeration
– Calculation of maximum non-zero shift Auto-
correlation of each code and cross-correlation
constraint of each pair of codes
– Formation of correlation matrix with diagonal
element as auto-correlation constraint and non-
diagonal element as cross-correlation constraint
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1 2( , ,..., )wa a a(1,1,...,n w 1) 
1 2 1( ) ( , ,..., ) 1w wi a a a a   ( ) ( 1).w
n
ii a n w
w
 
     

20. Design of Maximal Set of 1D
Uni-polar (Optical) Orthogonal Codes
 Algorithm One
– For given formation of reduced
correlation matrix having codes with maximum
non-zero shift auto-correlation constraint
– Calculation of upper bound ‘Z’ of the set with
code parameters with
as
– All the rows and column of reduced correlation
matrix with more than ‘Z’ non-diagonal elements
with entries are used to search final sets of
codes.
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a
a cand 
( , , , )a cn w   max( , )a c  
( 1)( 2)...( )
( 1)...( )
n n n
Z
w w w


   
    
c

21. Design of Maximal Set of 1D
Uni-polar (Optical) Orthogonal Codes
 Algorithm One
– Computational Complexity of the order
– Where
– Overall computational complexity
– which may be polynomial type for
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3
( )O r
 ( 1)( 2)...( 1)
( 1)( 2)...2.1
wn n n w n
ww w wr    
  
  3w
n
wO
w n

22. Design of Maximal Set of 1D
Uni-polar (Optical) Orthogonal Codes
 Algorithm Two
– Very similar to algorithm one till the generation
of all the codes in DoPR
– Calculation of auto-correlation constraint of all
the codes i.e. diagonal elements of correlation
matrix
– Find a reduced correlation matrix with the codes
having maximum non-zero shift autocorrelation
to be less than
– Using clique finding search method all the
maximal set with upper bound ‘Z’ can be found.
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a

23. Design of Maximal Set of 1D
Uni-polar (Optical) Orthogonal Codes
 Algorithm Two
– Computational Complexity of the order
– Where
– and
– Overall computational complexity
– which may be polynomial type for but
less complex than algorithm one.
– Results of both the algorithms can be verified in
Appendices of thesis.
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3
( )O r
w n
   ( 1)( 2)...( )
( 1)( 2)...
n n n n
ww w w w
r


  
  
 
 max ,a c  
  3
n
wO


24. Two Dimensional Uni-polar (Optical)
Orthogonal Codes
Weighted Position Representation (WPR)
– For L=4, N=5, w=7
– Example: X =
– WPR(X)= (1’0, 3’0, 2’1, 4’1, 1’4, 3’4, 4’4);
– For every column-wise circular shifting code X remain
same
– WPR (X)= (1’0, 3’0, 4’1, 2’2) = (4’0, 2’1, 1’4, 3’4) =
(2’0, 1’3, 3’3, 4’4) = (1’2, 3’2, 4’3, 2’4) = (1’1, 3’1, 4’2, 2’3) .
– No unique representation
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1 0 0 0 1
0 1 0 0 0
1 0 0 0 1
0 1 0 0 1
 
 
 
 
 
 

25. Two Dimensional Uni-polar (Optical)
Orthogonal Codes
Difference of Positions Representation
(DoPR), (proposed)
– For L=4, N=5, w=7,
– = WPR(1’0, 3’0, 2’1, 4’1, 1’4, 3’4, 4’4),
– X= = DoPR (1’0, 3’1, 2’0, 4’3, 1’0, 3’0, 4’1)
– For every column wise circular shifting
– X = = WPR(2’0, 4’0, 1’3, 3’3, 4’3, 1’4, 3’4),
– = DoPR (2’0, 4’3, 1’0, 3’0, 4’1, 1’0, 3’1)
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1 0 0 0 1
0 1 0 0 0
1 0 0 0 1
0 1 0 0 1
 
 
 
 
 
 
0 0 0 1 1
1 0 0 0 0
0 0 0 1 1
1 0 0 1 0
 
 
 
 
 
 

26. Two Dimensional Uni-polar (Optical)
Orthogonal Codes
Difference of Positions Representation
(DoPR)
X= = WPR(1’2, 3’2, 4’2, 1’3, 3’3, 2’4, 4’4),
= DoPR (1’0, 3’0, 4’1, 1’0, 3’1, 2’0, 4’3)
= WPR(1’1, 3’1, 4’1, 1’2, 3’2, 2’3, 4’3)
X= = DoPR (1’0, 3’0, 4’1, 1’0, 3’1, 2’0, 4’3)
=WPR(1’0, 3’0, 4’0, 1’1, 3’1, 2’2, 4’2)
X= =DoPR (1’0, 3’0, 4’1, 1’0, 3’1, 2’0, 4’3).
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0 0 1 1 0
0 0 0 0 1
0 0 1 1 0
0 0 1 0 1
 
 
 
 
 
 
0 1 1 0 0
0 0 0 1 0
0 1 1 0 0
0 1 0 1 0
 
 
 
 
 
 
1 1 0 0 0
0 0 1 0 0
1 1 0 0 0
1 0 1 0 0
 
 
 
 
 
 

27. Two Dimensional Uni-polar (Optical)
Orthogonal Codes
 Difference of Positions Representation (DoPR)
– In every column wise circular shifting of the code, WPR of
code changed but DoPR remain same, it is only circular
shifted versions of DoPR (1’0, 3’0, 4’1, 1’0, 3’1, 2’0, 4’3)
without changing the numerical values.
– Suppose DoPR (X)=
– then , where N is number of column
– DoPR = WPR
– Where
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 1 1 2 2' , ' ,..., 'w wa d a d a d
1 2 ... wd d d N   
 1 1 2 2' , ' ,..., 'w wa d a d a d  1 1 2 2' , ' ,..., 'w wa b a b a b
1
2 1 1
3 2 2
1 1
0;
;
;
...;
;w w w
b
b b d
b b d
b b d 

 
 
 

28. Two Dimensional Uni-polar (Optical)
Orthogonal Codes
 Calculation of Correlation Constraints
– If code X and Y are matrix binary sequences
– Maximum non-zero shift Auto-correlation of X
– Cross-correlation Constraint of X and Y
 Upper bound of the code set
– for
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1 1
, ,
0 0
, 0 1,
L N
i j i j a
i j
x x for N  
 

 
   
1 1
, ,
0 0
, 0 1.
L N
i j i j c
i j
x y for N  
 

 
   
 , , ,a cL N w  
   
1
, , , , ;
1
A
L LN LN
Z L N w J L N w
w w w

 

    
           
 max ,a c  

29. Two Dimensional Uni-polar (Optical)
Orthogonal Codes
 Calculation of Correlation Constraints
– If code X and Y are given in WPR
– Auto-correlation Constraint of code X
– Cross-correlation Constraint of code X,Y
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( ) ( ), (0 1)a P PX p X p N      
( ) ( ), (0 1)
( ) ( ), (0 1)
c P P
c P P
X p Y p N
Alternatively
Y p X p N


     
     

30. Two Dimensional Uni-polar (Optical)
Orthogonal Codes
 Calculation of Correlation Constraints
– Example for Auto-correlation:
– XP = = WPR (1’0, 3’0, 2’1, 4’1, 1’4, 3’4, 4’4),
 1+ XP = WPR (1’0, 3’0, 4’0, 1’1, 3’1, 2’2, 4’2),
 2+ XP = WPR (1’1, 3’1, 4’1, 1’2, 3’2, 2’3, 4’3),
 3+ XP = WPR (1’2, 3’2, 4’2, 1’3, 3’3, 2’4, 4’4),
 4+ XP = WPR(2’0, 4’0, 1’3, 3’3, 4’3, 1’4, 3’4),
– , , ,
– Maximum non-zero shift Auto-correlation
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1 0 0 0 1
0 1 0 0 0
1 0 0 0 1
0 1 0 0 1
 
 
 
 
 
 
( ) (1 ) 2P PX X   ( ) (2 ) 1P PX X   ( ) (3 ) 1P PX X   ( ) (4 ) 2P PX X  
2a 

31. Two Dimensional Uni-polar (Optical)
Orthogonal Codes
 Calculation of Correlation Constraints
– Example for Cross-correlation
– XP = = WPR (1’0, 3’0, 2’1, 4’1, 1’4, 3’4, 4’4),
and
– YP = = WPR (1’0, 2’0, 4’1, 2’2, 3’2, 1’4, 4’4),
 1+ YP = WPR (1’0, 4’0, 1’1, 2’1, 4’2, 2’3, 3’3),
 2+ YP = WPR (1’1, 4’1, 1’2, 2’2, 4’3, 2’4, 3’4),
 3+ YP = WPR (2’0, 3’0, 1’2, 4’2, 1’3, 2’3, 4’4),
 4+ YP = WPR (4’0, 2’1, 3’1, 1’3, 4’3, 1’4, 2’4),
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1 0 0 0 1
0 1 0 0 0
1 0 0 0 1
0 1 0 0 1
 
 
 
 
 
 
1 0 0 0 1
1 0 1 0 0
0 0 1 0 0
0 1 0 0 1
 
 
 
 
 
 

32. Two Dimensional Uni-polar (Optical)
Orthogonal Codes
 Calculation of Correlation Constraints
– Example for Cross-correlation (continued…)
– Cross-correlation constraint for pair of codes X and Y be
– If X and Y generated in DoPR, first the codes will be
converted into WPR and then calculation of correlation
constraints of the codes is done.
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( ) (1 ) 2P PX Y   ( ) (2 ) 2P PX Y  
( ) (3 ) 2P PX X   ( ) (4 ) 2P PX X  
2c 

33. Design of Maximal Set of 2D
Uni-polar (Optical) Orthogonal Codes
 Algorithm One
– For code length ‘n=LN’ and code weight ‘w’, all
the one dimensional codes in standard DoPR
are generated starting from to
with enumeration
– (i) Conversion of one dimensional code (DoPR)
Into into corresponding one dimensional code (WPR)
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1 2( , ,..., )wm m m
(1,1,...,n w 1) 
1 2 1( ) ( , ,..., ) 1w wi m m m m   ( ) ( 1).w
n
ii m n w
w
 
     
1 2( , ,..., )wm m m
1 1 2 1 2 1(1, 1, 1,...,1 ... )wm m m m m m       

34. Design of Maximal Set of 2D
Uni-polar (Optical) Orthogonal Codes
 Algorithm One
– Conversion of one dimensional code (WPR) into two
dimensional code (WPR) by dividing each weighted
position by ‘L’ to get quotient ‘b’ and remainder ‘a’ for each
weighted position. Here each a’b represent to each
weighted position in matrix orthogonal code. ‘a’ stands for
row position and ‘b’ stands for column position.
 Lemma 5.4.1.1:
The matrix orthogonal code with a’b weighted positions can be
converted into corresponding binary matrix orthogonal code by
putting binary digit ‘1’ at weighted positions and ‘0’ otherwise. This
binary matrix orthogonal code can be converted into ‘L’ binary matrix
orthogonal codes by every row wise circular shifting of the code.
 Conversion of two dimensional code (WPR) into two dimensional
code (DoPR) by getting difference ‘d’ of two columns of consecutive
weighted positions and vice versa.
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35. Design of Maximal Set of 2D
Uni-polar (Optical) Orthogonal Codes
 Algorithm One
– Calculation of auto-correlation constraint of each code
generated
– Calculation of cross-correlation constraint of each pair of
codes
– Formation of correlation matrix with diagonal element as
maximum non-zero shift autocorrelation values and cross-
correlation constraint values over non-diagonal elements.
– Formation of reduced correlation matrix with the codes
having maximum non-zero shift auto-correlation less than
or equal to given auto-correlation constraint
– Calculation of upper bound of the set
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a
   
1
, , , , ;
1
A
L LN LN
Z L N w J L N w
w w w

 

    
           
 , , ,a cL N w  
 max ,a c  

36. Design of Maximal Set of 2D
Uni-polar (Optical) Orthogonal Codes
 Algorithm One (continued…)
– From the reduced correlation matrix only those rows and
columns are selected whose number of cross-correlation
entries being greater than the upper bound Z of the sets of
codes to be generated.
– In this reduced correlation matrix, number of rows or
columns are equal to P. Out of these P codes, all possible
combinations of sets of non repeated Z codes are formed
mentioning their code numbers. These possible
combinations of sets are equal to
– Each such set of codes are checked for their maximum
cross-correlation constraint through the use of cross-
correlation entries from reduced correlation matrix. It will
achieve final sets of codes as required.
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( 1)...( 1)
( 1)...2.1
P
Z
P P P Z
G C
Z Z
  
 

c

37. Design of Maximal Set of 2D
Uni-polar (Optical) Orthogonal Codes
 Algorithm One
– Computational Complexity
• Of the order
• Where
• Overall computation complexity
• Which may be polynomial type for
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3
( )O r
 ( 1)( 2)...( 1)
( 1)( 2)...2.1
wLN LN LN w LN
ww w wr    
  
  3w
LN
wO
w LN

38. Design of Maximal Set of 2D
Uni-polar (Optical) Orthogonal Codes
 Algorithm Two
– Very similar to algorithm one till the generation
of all the codes in WPR/DoPR
– Calculation of auto-correlation constraint of all
the codes i.e. diagonal elements of correlation
matrix
– Find a reduced correlation matrix with the codes
having maximum non-zero shift autocorrelation
to be less than
– Using clique finding search method all the
maximal set with upper bound ‘Z’ can be found.
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a

39. Design of Maximal Set of 2D
Uni-polar (Optical) Orthogonal Codes
 Algorithm Two
– Computational Complexity of the order
– Where
– and
– Overall computational complexity
– which may be polynomial type for but
less complex than algorithm one.
– Results of both the algorithms can be verified in
Appendices of thesis.
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3
( )O r
w LN
   (LN 1)(LN 2)...(LN )
( 1)( 2)...
LN
ww w w w
r


  
  
 
 max ,a c  
  3
LN
wO


40. Summary of Results
 Appendix I : Algorithm one designing 1D
UOC
 Appendix II : Algorithm two designing 1D
UOC
 Appendix III : Algorithm one designing 2D
UOC
 Appendix IV : Algorithm two designing 2D
UOC
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41. Table of Comparisons
 Table 2.1: Comparison of already proposed 1-D
OOCs design schemes with ideal scheme.
 Table 3.1: Comparison of proposed algorithms with
ideal scheme for generating 1-D UOCs
 Table 4.1: Comparison of proposed 2-D OOCs
design schemes with ideal one.
 Table 5.1: Comparison of proposed algorithms with
ideal scheme for generating 2-D UOCs
 Table 6.1: Comparison of proposed algorithms for
generating 1-D and 2-D UOCs.
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42. Conclusions
 Advantages and disadvantages of UOCs
(1-D & 2-D)
 Comparisons of UOCs (1-D & 2-D)
 Cardinality and orthogonality of the set of
codes and multiple access interference.
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43. Future Directions
 Multi-dimensional UOC
 Applications not only limited to OCDMA
 Computational complexity of algorithms can
be reduced upto some extent.
 Multiple access interference reduction
schemes can be proposed for codes with
higher value of correlation constraints.
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44. References
 [1] Prucnal P. R., “ Optical Code Division Multiple Access:
Fundamentals and Applications,” CRC Press, Taylor & Francis
Group, first edition, 2006.
 [25] Chung, F.R.K., Salehi, J., Wei, V.K. “Optical orthogonal
codes: Design, analysis and applications,” IEEE Transactions
on Information Theory, vol. 35, no. 3, 1989, pp. 595–604.
 [65] M. Choudhary, P. K. Chatterjee, and J. John, “Code
sequences for fiber optic CDMA systems,” In: Proceedings of
National Conference on Communications, IIT Kanpur, 1995, pp.
35-42.
 [90] M. Choudhary, P.K. Chatterjee, and J. John, “Optical
orthogonal codes using hadamard matices,” in Proc. of
National Conference on Communication, IIT Kanpur, 2001, pp.
209-211.
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45. References
 [101] Sargent, E., Stok, A.,“The role of optical CDMA in access
network,” IEEE Communications Magazine, vol. 40, no. 9, 2002,
pp. 83–87.
 [109] J.Shah, “Optical CDMA,” Optics & Photonics News ,
vol. 14, April 2003, pp. 42-47.
 [132] E.S.Shivaleela, A.Shelvarajan, T. Srinivas; “Two
Dimensional Optical Orthogonal Codes for Fiber-Optic CDMA
Networks,” Journal of Lightwave Technology, Vol.23, No.2, Feb
2005, pp. 647 – 654.
 [133] Reja Omrani and P.Vijay Kumar; “Codes for Optical
CDMA” SETA 2006, LNCS 4086, 2006, pp. 34-46.
 [154] Y C Lin, G C Yang, C Y Chang, W C Kwong “Construction
of optimal 2D optical codes using (n,w,2,2) optical orthogonal
codes” IEEE Transactions on Communications, vol. 59, no. 1,
January 2011, pp. 194–200.
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46. Publications
[1] R. C. S. Chauhan, R. Asthana, Y. N. Singh, “A General Algorithm to
Design Sets of All Possible One Dimensional Unipolar orthogonal codes
of Same Code Length and Weight,” 2010 IEEE International
Conference on Computational Intelligence and Computing Research
(ICCIC-2010), Coimbatore, India, IEEE conference proceedings, 978-
1-4244-5966-7/10, 28-29 December 2010, pp. 7-13.
[2] R. C. S. Chauhan, R. Asthana, Y. N. Singh, “Unipolar Orthogonal
Codes: Design, Analysis and Applications” International Conference
on High Performance Computing (HiPC-2010), Student Research
Symposium, 19-22 December 2010, Goa, India.
[3] R. C. S. Chauhan, R. Asthana, “Representation and calculation of
correlation constraints of one dimensional unipolar orthogonal codes
(1-D UOC),” IEEE International Conference CSNT-2011, Jammu,
India on 3 – 5 June 2011. IEEE conference proceedings, 978-1-4577-
0543-4 , 3 – 5 June 2011, pp. 483-489.
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UPTU/PhD/07/EC/539 46

47. Publications
[4] R. C. S. Chauhan, Y. N. Singh, R. Asthana, “A Search Algorithm to
Find Multiple Sets of One Dimensional Unipolar orthogonal Codes
with Same Code Length and low Weight,” Journal of Computing
Technologies, Vol 2, Issue 9, September 2013, pp. 12-19.
[5] R. C. S. Chauhan, Y. N. Singh, R. Asthana, “Design of Two
Dimensional Unipolar (Optical) Orthogonal Codes Through One
Dimensional Unipolar (Optical) Orthogonal Codes,” Journal of
Computing Technologies, Vol 2, Issue 9, September 2013, pp. 20-24.
[6] R. C. S. Chauhan, Y. N. Singh, R. Asthana, “Design of Minimum
Correlated, Maximal Clique Sets of One Dimensional Unipolar
(Optical) Orthogonal codes” arXiv preprint arxiv: 1309.0193, 2013.
[7] R. C. S. Chauhan, Y. N. Singh, R. Asthana, “Design of Minimum
Correlated, Maximal Clique Sets of Two Dimensional
Unipolar (Optical) Orthogonal codes” Under Review
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UPTU/PhD/07/EC/539 47

48. Thanks
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UPTU/PhD/07/EC/539 48

49. Design of Unipolar (Optical) Orthogonal
Codes and Their Maximal Clique Sets
by
Ram Chandra Singh Chauhan
(PhD/07/EC/539)
Under the Supervision of
Dr. Y.N. Singh Dr. R. Asthana
Professor Associate Professor
IIT, Kanpur HBTI, Kanpur
to
Faculty of Engineering & Technology
UPTU, Lucknow
July 11, 2015