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  • pg 1
									     Synchronous Walsh-Based Bipolar–Bipolar Code for
           CDMA Passive Optical Networks

               Advisor : Jen - Fa Huang
                 Student : Da-Jun Nie

            H.-W. Hu, H.-T. Chen, G.-C. Yang, W. C. Kwong,
“Synchronous Walsh-Based Bipolar–Bipolar Code for CDMA Passive Optical
                                 Networks”
       J. Lightw. Technol., vol. 25, no.8, pp.1910-1917, Aug. 2007
                              2007/9/27                                  1
               Outline
   Introduction
   Construction of the 2-D Walsh Bipolar-
    Bipolar code
   AWG encoder/decoder
   Performance Analysis
   Conclusion



                                             2
                  Introduction (1)
 For OCDMA, the three most important parameters are the
  number of simultaneous users, the number of possible
  subscribers, and the error probability as a function of multiple-
  access interference (MAI).

 Two-dimensional wavelength-time codes increase the number
  of subscribers and simultaneous users by utilizing two coding
 dimensions (namely time and wavelength) simultaneously, rather
 than only one coding dimension in 1-D optical codes.




                                                                      3
               Introduction (2)
 This paper shows that the Walsh-based bipolar–bipolar
  code supports more subscribers and simultaneous users
  (i.e., better performance) at the expense of requiring
  synchronization.
 The downstream traffic is synchronous in nature, while
 the upstream traffic is asynchronous.
 That is, synchronous downstream traffic uses the
 Walsh-based bipolar–bipolar code, and asynchronous
  upstream traffic uses the Barker-based bipolar–
  bipolar code.




                                                           4
  Construction of the 2-D Walsh Bipolar-Bipolar code

Multiwavelength Codeword Based on walsh Code of Length m=16




                                                              5
       Synchronized Prime sequence over GF(11)




j   0 1 2 3 4 5 6 7 8 9 10


     si , j  i  j           si , j ,l  (i  j )  l
                             Ex. s1,6,8  (1  6)  8  14


                                                             6
  Synchronized Prime sequence properties

(1) The cross-correlational function is at most one
    for any two prime sequences that originated
    from different groups
(2) The cross-correlational function at the
    synchronized (i.e.,nonshifted) position is zero
    for any two prime sequences that originated
    from the same group




                                                      7
    2D Bipolar-Bipolar Matrices

Based on GF(11), Multiwavelength Codewords of Length m = 16,
Time-Spreading Walsh Sequence 10101010 of Length n = 8




                                                               8
Code#12
Bit 1 #12:C1C2C3C4C5C6C7C8   Bit 0         CCCCCCCC
                                            1 2 3 4 5 6 7 8
     15                             15
     14                             14
     13                             13
     12                             12
     11                             11
     10                             10
     9                              9
     8                              8
     7                              7
     6                              6
     5                              5
     4                              4
     3                              3
     2                              2
     1                              1
     0                              0                       9
                       AWG encoder
                         #12:C1C2C3C4C5C6C7C8
                               C1


                               C2
  Assume    USER#1 #12

                               C3




                               C8


      For Example:
                          C3        0          reflector
                                                absorber
                                    1
                                    2
0123......1415
                                    15         reflector
                                                absorber

                                                            10
                        AWG encoder
 Tunable encoder 1
  Switch control 1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0
  Reflector : C0  0 , 2 , 4 , 6 , 8 , 10 , 12 , 14 
   Absorber :       C0  1 , 3 , 5 , 7 , 9 , 11 , 13 , 15 
Tunable encoder 2
  Switch control 1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0
     Reflector :      C1  0 , 1, 4 , 5 , 8 , 9 , 12 , 13
     Absorber :       C1  2 , 3 , 6 , 7 , 10 , 11 , 14 , 15 
         
         



                                               C C C C C C C C 
         

  經過Delay Line 可得 user 11 =                         0   1   2   3   4   5   6   7
                                                                                    11
                           AWG decoder
For Example:
                                +1


                                +1    +8
 #12:C1C2C3C4C5C6C7C8
                                +1
                                                     Bit 1
   40、81、42...215
                                 +1




          Decoder for C3
                                           16units


         C3、C5、C8                                      7units→+1
   →30、21、22、3、4                      9units
   、26、7、28、39、10
   、211、213、14、215


                                                               12
                            AWG decoder
                           C0  1 , 2 , 4 , 6 , 8 , 10 , 12 , 14 
                           C1  0 , 1 , 4 , 5 , 8 , 9 , 12 , 13 
                           C2  0 , 3 , 4 , 7 , 8 , 11 , 12 , 15 
                           C3  0 , 1 , 2 , 3 , 8 , 9 , 10 , 11

               The received wavelengths in one time slot are
   40 , 21, 22 , 23 ,34 , 5 , 6 , 7 , 48 , 29 , 210 , 211,312 , 13 , 14 , 15
decoder designed for receiving C0  1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0
  the top photodetector is              48  29  210  211  312  13  14  15  16 units

  the bottom photodetector is 21  23  5  7  29  211  13  15  12 units
  The balanced detector performs subtraction and finally gives an
  autocorrelation peak of 20-12 = 8 units of electrical current.
                                                                                                      13
 decoder designed for receiving C0  0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1
 the top photodetector is       21  23  5  7  29  211  13  15  12 units

the bottom photodetector is 40  22  34  6  48  210 312  14  20 units

  The balanced detector performs subtraction and finally gives an
  autocorrelation peak of 12-20 = -8 units of electrical current.


decoder designed for receiving              C7  1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0
  the top photodetector is       40  21  22  23  34  5  6  7  16 units

 the bottom photodetector is 48  29  210  211  312  13  14  15  16             units


  The balanced detector performs subtraction and finally gives an
  autocorrelation peak of 16-16 = 0 units of electrical current.
                                                                                          14
                      Cardinality
The cardinality  t of the Walsh code of length n selected for
time spreading is given by  t = n.
                                                   p2
Since the number of synchronized prime sequences is over GF(p) for a
prime p, the overall cardinality of the final Walsh based bipolar–bipolar
code is
           Walsh   t p  np2        2
                                               (ex. 8 112  968)




                                                                            15
             Performance Analysis
                                                  n2
               Pe  Q( SIR )  Q(                     2
                                                          )
                                                  
Variances of the Walsh-Based Bipolar–Bipolar Code
       2                np    2                 K  np    2
       Walsh , syn         Walsh ,syn ,np           Walsh ,syn , jnp
                        K                         K
• Variance of the cross-correlational functions when
      Walsh.syn> np such that
                  2                     n( jp  p ) t2 n
                 Walsh , syn , jnp                  1
                                                        
                                            njp  1       p

                                                                              16
         Performance Analysis
• For the special case of supporting at most np users
             2                np  2
             Walsh , syn       Walsh,syn,np  0
                              K
• For the case of the maximum cardinality             Walsh.syn  np   2

   , the average variance

              2                n( p 2  p ) t12 n
              Walsh , syn                     
                                   np  1
                                       2
                                                  p



                                                                            17
          Numerical Examples (1)
assume that simultaneous users select code matrices
group-by-group




                                                      18
       Numerical Examples (2)
assume that simultaneous users randomly select code matrices




                                                               19
                     Conclusion
   The analysis showed that the new synchronous coding
    scheme supported larger cardinality and better performance
    than the original asynchronous Barker-based bipolar–bipolar
    code.
   The Walsh-based bipolar–bipolar code found an application
    in the synchronous downstream traffic in the future CDMA-
    based PONs, while asynchronous upstream traffic used the
    Barker-based bipolar–bipolar code.




                                                                  20
              Performance Analysis
For comparison, the overall cardinality of the Barker-based bipolar–bipolar
code is given by

               Bar ker  p       2


The cardinality is smaller than because there is only one Barker
sequence (i.e.,  t = 1) for any given length.




                                                                              21
                                  Performance Analysis
       Variances of the Barker-Based Bipolar–Bipolar Code
              2             p   2                  Kp    2
             Bar ker,asyn    Bar ker,asyn, p        Bar ker,asyn, jp
                            K                       K
    •Variance of the cross-correlational functions when  Bar ker,asyn  p
                                         2                         p  1 ( K  1)
                                            Bar ker, asyn , p         
                                                                    p       n
•Variance of the cross-correlational functions when  Bar ker,asyn  p

                              1  ( jp  p) p1 n  j  1  ( p  1) t 2 2 ( jp  p) p 2 2 n 
                                               2
    2
       Bar ker, asyn , jp                                                          
                              j 
                                      jp  1     p
                                                     j     jp  1
                                                                                jp  1      p


                                                                                              22
              Performance Analysis
• For the case of the maximum cardinality of Bar ker,asyn  p2
  the average variance

                           1  ( p  p) p1 n  p  1
                                  2        2
      2
         Bar ker, asyn                    
                           p 
                                   p 1
                                     2
                                              p
                                                 p

                             ( p  1) t 2 2 ( p 2  p) p 2 2 n 
                                                             
                             p 1                  p 1
                                   2                 2
                                                               p




                                                                      23

								
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