Abstract

A novel family of codes for modified spectral-amplitude-coding optical code division multiple access (SAC-OCDMA) is introduced. The proposed codes exist for more processing gains than the previously reported codes do. In the network using these codes, the number of users can be extended without any essential changes in the previous transmitters. In this study, we propose a construction method for these codes and compare their performance with previously reported codes.

© 2010 Optical Society of America

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References

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  1. D. Zaccarin, M. Kavehrad, “An optical CDMA system based on spectral encoding of LED,” IEEE Photon. Technol. Lett., vol. 4, pp. 479–482, Apr. 1993.
    [CrossRef]
  2. E. D. J. Smith, R. J. Blaikie, D. P. Taylor, “Performance enhancement of spectral-amplitude-coding optical CDMA using pulse-position modulation,” IEEE Trans. Commun., vol. 46, no. 9, pp. 1176–1185, Sept. 1998.
    [CrossRef]
  3. E. D. J. Smith, P. T. Gough, D. P. Taylor, “Noise limits of optical spectral-encoding CDMA systems,” Electron. Lett., vol. 31, no. 17, pp. 1469–1470, Aug. 1995.
    [CrossRef]
  4. X. Zhou, H. M. H. Shalaby, C. Lu, T. Cheng, “Code for spectral amplitude coding optical CDMA systems,” Electron. Lett., vol. 36, pp. 728–729, Apr. 2000.
    [CrossRef]
  5. Z. Wei, H. Ghafouri-Shiraz, H. M. H. Shalaby, “New code families for fiber-Bragg-grating-based spectral-amplitude-coding optical CDMA systems,” IEEE Photon. Technol. Lett., vol. 13, pp. 890–892, Aug. 2001.
    [CrossRef]
  6. Z. Wei, H. Ghafouri-Shiraz, “Proposal of a novel code for spectral amplitude-coding optical CDMA systems,” IEEE Photon. Technol. Lett., vol. 14, no. 3, pp. 414–416, Mar. 2002.
    [CrossRef]
  7. I. B. Djordjevic, B. Vasic, “Unipolar codes for spectral-amplitude-coding optical CDMA systems based on projective geometries,” IEEE Photon. Technol. Lett., vol. 15, no. 9, pp. 1318–1320, Sept. 2003.
    [CrossRef]
  8. S. A. Aljunid, M. Ismail, A. R. Ramli, B. M. Ali, M. K. Abdullah, “A new family of optical code sequences for spectral-amplitude-coding optical CDMA systems,” IEEE Photon. Technol. Lett., vol. 16, pp. 2383–2385, Oct. 2004.
    [CrossRef]
  9. C. H. Lin, J. Wu, H. W. Tsao, C. L. Yang, “Spectral amplitude-coding optical CDMA system using Mach–Zehnder interferometers,” J. Lightwave Technol., vol. 23, no. 4, pp. 1543–1555, Apr. 2005.
    [CrossRef]
  10. M. Rochette, S. Ayotte, L. A. Rusch, “Analysis of the spectral efficiency of frequency-encoded OCDMA system with incoherent sources,” J. Lightwave Technol., vol. 23, no. 4, pp. 1610–1619, Apr. 2005.
    [CrossRef]
  11. B. Moslehi, “Analysis of optical phase noise in fiber optic systems employing a laser source with arbitrary coherence time,” J. Lightwave Technol., vol. 4, no. 9, pp. 1334–1351, Sept. 1986.
    [CrossRef]

2005

2004

S. A. Aljunid, M. Ismail, A. R. Ramli, B. M. Ali, M. K. Abdullah, “A new family of optical code sequences for spectral-amplitude-coding optical CDMA systems,” IEEE Photon. Technol. Lett., vol. 16, pp. 2383–2385, Oct. 2004.
[CrossRef]

2003

I. B. Djordjevic, B. Vasic, “Unipolar codes for spectral-amplitude-coding optical CDMA systems based on projective geometries,” IEEE Photon. Technol. Lett., vol. 15, no. 9, pp. 1318–1320, Sept. 2003.
[CrossRef]

2002

Z. Wei, H. Ghafouri-Shiraz, “Proposal of a novel code for spectral amplitude-coding optical CDMA systems,” IEEE Photon. Technol. Lett., vol. 14, no. 3, pp. 414–416, Mar. 2002.
[CrossRef]

2001

Z. Wei, H. Ghafouri-Shiraz, H. M. H. Shalaby, “New code families for fiber-Bragg-grating-based spectral-amplitude-coding optical CDMA systems,” IEEE Photon. Technol. Lett., vol. 13, pp. 890–892, Aug. 2001.
[CrossRef]

2000

X. Zhou, H. M. H. Shalaby, C. Lu, T. Cheng, “Code for spectral amplitude coding optical CDMA systems,” Electron. Lett., vol. 36, pp. 728–729, Apr. 2000.
[CrossRef]

1998

E. D. J. Smith, R. J. Blaikie, D. P. Taylor, “Performance enhancement of spectral-amplitude-coding optical CDMA using pulse-position modulation,” IEEE Trans. Commun., vol. 46, no. 9, pp. 1176–1185, Sept. 1998.
[CrossRef]

1995

E. D. J. Smith, P. T. Gough, D. P. Taylor, “Noise limits of optical spectral-encoding CDMA systems,” Electron. Lett., vol. 31, no. 17, pp. 1469–1470, Aug. 1995.
[CrossRef]

1993

D. Zaccarin, M. Kavehrad, “An optical CDMA system based on spectral encoding of LED,” IEEE Photon. Technol. Lett., vol. 4, pp. 479–482, Apr. 1993.
[CrossRef]

1986

B. Moslehi, “Analysis of optical phase noise in fiber optic systems employing a laser source with arbitrary coherence time,” J. Lightwave Technol., vol. 4, no. 9, pp. 1334–1351, Sept. 1986.
[CrossRef]

Abdullah, M. K.

S. A. Aljunid, M. Ismail, A. R. Ramli, B. M. Ali, M. K. Abdullah, “A new family of optical code sequences for spectral-amplitude-coding optical CDMA systems,” IEEE Photon. Technol. Lett., vol. 16, pp. 2383–2385, Oct. 2004.
[CrossRef]

Ali, B. M.

S. A. Aljunid, M. Ismail, A. R. Ramli, B. M. Ali, M. K. Abdullah, “A new family of optical code sequences for spectral-amplitude-coding optical CDMA systems,” IEEE Photon. Technol. Lett., vol. 16, pp. 2383–2385, Oct. 2004.
[CrossRef]

Aljunid, S. A.

S. A. Aljunid, M. Ismail, A. R. Ramli, B. M. Ali, M. K. Abdullah, “A new family of optical code sequences for spectral-amplitude-coding optical CDMA systems,” IEEE Photon. Technol. Lett., vol. 16, pp. 2383–2385, Oct. 2004.
[CrossRef]

Ayotte, S.

Blaikie, R. J.

E. D. J. Smith, R. J. Blaikie, D. P. Taylor, “Performance enhancement of spectral-amplitude-coding optical CDMA using pulse-position modulation,” IEEE Trans. Commun., vol. 46, no. 9, pp. 1176–1185, Sept. 1998.
[CrossRef]

Cheng, T.

X. Zhou, H. M. H. Shalaby, C. Lu, T. Cheng, “Code for spectral amplitude coding optical CDMA systems,” Electron. Lett., vol. 36, pp. 728–729, Apr. 2000.
[CrossRef]

Djordjevic, I. B.

I. B. Djordjevic, B. Vasic, “Unipolar codes for spectral-amplitude-coding optical CDMA systems based on projective geometries,” IEEE Photon. Technol. Lett., vol. 15, no. 9, pp. 1318–1320, Sept. 2003.
[CrossRef]

Ghafouri-Shiraz, H.

Z. Wei, H. Ghafouri-Shiraz, “Proposal of a novel code for spectral amplitude-coding optical CDMA systems,” IEEE Photon. Technol. Lett., vol. 14, no. 3, pp. 414–416, Mar. 2002.
[CrossRef]

Z. Wei, H. Ghafouri-Shiraz, H. M. H. Shalaby, “New code families for fiber-Bragg-grating-based spectral-amplitude-coding optical CDMA systems,” IEEE Photon. Technol. Lett., vol. 13, pp. 890–892, Aug. 2001.
[CrossRef]

Gough, P. T.

E. D. J. Smith, P. T. Gough, D. P. Taylor, “Noise limits of optical spectral-encoding CDMA systems,” Electron. Lett., vol. 31, no. 17, pp. 1469–1470, Aug. 1995.
[CrossRef]

Ismail, M.

S. A. Aljunid, M. Ismail, A. R. Ramli, B. M. Ali, M. K. Abdullah, “A new family of optical code sequences for spectral-amplitude-coding optical CDMA systems,” IEEE Photon. Technol. Lett., vol. 16, pp. 2383–2385, Oct. 2004.
[CrossRef]

Kavehrad, M.

D. Zaccarin, M. Kavehrad, “An optical CDMA system based on spectral encoding of LED,” IEEE Photon. Technol. Lett., vol. 4, pp. 479–482, Apr. 1993.
[CrossRef]

Lin, C. H.

Lu, C.

X. Zhou, H. M. H. Shalaby, C. Lu, T. Cheng, “Code for spectral amplitude coding optical CDMA systems,” Electron. Lett., vol. 36, pp. 728–729, Apr. 2000.
[CrossRef]

Moslehi, B.

B. Moslehi, “Analysis of optical phase noise in fiber optic systems employing a laser source with arbitrary coherence time,” J. Lightwave Technol., vol. 4, no. 9, pp. 1334–1351, Sept. 1986.
[CrossRef]

Ramli, A. R.

S. A. Aljunid, M. Ismail, A. R. Ramli, B. M. Ali, M. K. Abdullah, “A new family of optical code sequences for spectral-amplitude-coding optical CDMA systems,” IEEE Photon. Technol. Lett., vol. 16, pp. 2383–2385, Oct. 2004.
[CrossRef]

Rochette, M.

Rusch, L. A.

Shalaby, H. M. H.

Z. Wei, H. Ghafouri-Shiraz, H. M. H. Shalaby, “New code families for fiber-Bragg-grating-based spectral-amplitude-coding optical CDMA systems,” IEEE Photon. Technol. Lett., vol. 13, pp. 890–892, Aug. 2001.
[CrossRef]

X. Zhou, H. M. H. Shalaby, C. Lu, T. Cheng, “Code for spectral amplitude coding optical CDMA systems,” Electron. Lett., vol. 36, pp. 728–729, Apr. 2000.
[CrossRef]

Smith, E. D. J.

E. D. J. Smith, R. J. Blaikie, D. P. Taylor, “Performance enhancement of spectral-amplitude-coding optical CDMA using pulse-position modulation,” IEEE Trans. Commun., vol. 46, no. 9, pp. 1176–1185, Sept. 1998.
[CrossRef]

E. D. J. Smith, P. T. Gough, D. P. Taylor, “Noise limits of optical spectral-encoding CDMA systems,” Electron. Lett., vol. 31, no. 17, pp. 1469–1470, Aug. 1995.
[CrossRef]

Taylor, D. P.

E. D. J. Smith, R. J. Blaikie, D. P. Taylor, “Performance enhancement of spectral-amplitude-coding optical CDMA using pulse-position modulation,” IEEE Trans. Commun., vol. 46, no. 9, pp. 1176–1185, Sept. 1998.
[CrossRef]

E. D. J. Smith, P. T. Gough, D. P. Taylor, “Noise limits of optical spectral-encoding CDMA systems,” Electron. Lett., vol. 31, no. 17, pp. 1469–1470, Aug. 1995.
[CrossRef]

Tsao, H. W.

Vasic, B.

I. B. Djordjevic, B. Vasic, “Unipolar codes for spectral-amplitude-coding optical CDMA systems based on projective geometries,” IEEE Photon. Technol. Lett., vol. 15, no. 9, pp. 1318–1320, Sept. 2003.
[CrossRef]

Wei, Z.

Z. Wei, H. Ghafouri-Shiraz, “Proposal of a novel code for spectral amplitude-coding optical CDMA systems,” IEEE Photon. Technol. Lett., vol. 14, no. 3, pp. 414–416, Mar. 2002.
[CrossRef]

Z. Wei, H. Ghafouri-Shiraz, H. M. H. Shalaby, “New code families for fiber-Bragg-grating-based spectral-amplitude-coding optical CDMA systems,” IEEE Photon. Technol. Lett., vol. 13, pp. 890–892, Aug. 2001.
[CrossRef]

Wu, J.

Yang, C. L.

Zaccarin, D.

D. Zaccarin, M. Kavehrad, “An optical CDMA system based on spectral encoding of LED,” IEEE Photon. Technol. Lett., vol. 4, pp. 479–482, Apr. 1993.
[CrossRef]

Zhou, X.

X. Zhou, H. M. H. Shalaby, C. Lu, T. Cheng, “Code for spectral amplitude coding optical CDMA systems,” Electron. Lett., vol. 36, pp. 728–729, Apr. 2000.
[CrossRef]

Electron. Lett.

E. D. J. Smith, P. T. Gough, D. P. Taylor, “Noise limits of optical spectral-encoding CDMA systems,” Electron. Lett., vol. 31, no. 17, pp. 1469–1470, Aug. 1995.
[CrossRef]

X. Zhou, H. M. H. Shalaby, C. Lu, T. Cheng, “Code for spectral amplitude coding optical CDMA systems,” Electron. Lett., vol. 36, pp. 728–729, Apr. 2000.
[CrossRef]

IEEE Photon. Technol. Lett.

Z. Wei, H. Ghafouri-Shiraz, H. M. H. Shalaby, “New code families for fiber-Bragg-grating-based spectral-amplitude-coding optical CDMA systems,” IEEE Photon. Technol. Lett., vol. 13, pp. 890–892, Aug. 2001.
[CrossRef]

Z. Wei, H. Ghafouri-Shiraz, “Proposal of a novel code for spectral amplitude-coding optical CDMA systems,” IEEE Photon. Technol. Lett., vol. 14, no. 3, pp. 414–416, Mar. 2002.
[CrossRef]

I. B. Djordjevic, B. Vasic, “Unipolar codes for spectral-amplitude-coding optical CDMA systems based on projective geometries,” IEEE Photon. Technol. Lett., vol. 15, no. 9, pp. 1318–1320, Sept. 2003.
[CrossRef]

S. A. Aljunid, M. Ismail, A. R. Ramli, B. M. Ali, M. K. Abdullah, “A new family of optical code sequences for spectral-amplitude-coding optical CDMA systems,” IEEE Photon. Technol. Lett., vol. 16, pp. 2383–2385, Oct. 2004.
[CrossRef]

D. Zaccarin, M. Kavehrad, “An optical CDMA system based on spectral encoding of LED,” IEEE Photon. Technol. Lett., vol. 4, pp. 479–482, Apr. 1993.
[CrossRef]

IEEE Trans. Commun.

E. D. J. Smith, R. J. Blaikie, D. P. Taylor, “Performance enhancement of spectral-amplitude-coding optical CDMA using pulse-position modulation,” IEEE Trans. Commun., vol. 46, no. 9, pp. 1176–1185, Sept. 1998.
[CrossRef]

J. Lightwave Technol.

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Figures (10)

Fig. 1
Fig. 1

Scheme of spectral amplitude coding.

Fig. 2
Fig. 2

Balanced receiver structure.

Fig. 3
Fig. 3

Differentiating receiver structure.

Fig. 4
Fig. 4

Structure of the proposed system.

Fig. 5
Fig. 5

(a) Marked set and (b) detection set of a user.

Fig. 6
Fig. 6

Distance between the “1” transmitting users.

Fig. 7
Fig. 7

Simulation and analytical results of the BER for the proposed codes.

Fig. 8
Fig. 8

Analytical results of the BER versus the number of active users for different code lengths.

Fig. 9
Fig. 9

Simulation results for MQC ( p = 11 ) , MFH ( q = 9 ) , and EPD ( F = 91 , F = 133 ) codes.

Fig. 10
Fig. 10

Simulation results for MQC ( p = 11 and p = 13 ) and EPD ( F = 133 and F = 183 ) codes.

Tables (5)

Tables Icon

Table 1 Code Words With F = 7 and w = 3

Tables Icon

Table 2 Codes With Fixed In-Phase Cross-Correlation for SAC Systems

Tables Icon

Table 3 Marked Sets and Detection Sets of EPD Codes for F = 7 , w = 2 , v = 2 , and s = 1

Tables Icon

Table 4 Marked Sets and Detection Sets of EPD Codes for F = 7 , w = 2 , v = 2 , and s = 2

Tables Icon

Table 5 Parameters Used in the Simulation and Numerical Calculations

Equations (76)

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k = 1 F a k b k = λ .
A i ( υ ) = k = 1 F A i k π [ ( υ υ 0 Δ υ ) ( k F + 1 2 ) ] ,
π ( x ) = { 0 | x | > 1 2 1 | x | 1 2 } .
X = i A 1 I ( λ i ) λ w λ i A 1 I ( λ i ) ,
F = { 3 2 N even N 3 2 N + 1 2 odd N } .
F = 3 N + 8 3 [ sin ( N π 3 ) ] 2 .
( M P 2 , P 1 M , 1 ) ,
{ A i , A j } = k = 1 F A i k A j k = { λ 1 i j F w i = j } ,
A ( υ ) B ( υ ) .
B i ( υ ) = k = 1 F B i k π [ ( υ υ 0 Δ υ ) ( k F + 1 2 ) ] ,
{ A i , B j } = k = 1 F A i k B j k = { λ 1 i j F w i = j } .
A j = { A i 1 ( j i ) , A i 2 ( j i ) , , A i F ( j i ) } ,
B j = { B i 1 ( j i ) , B i 2 ( j i ) , , B i F ( j i ) } ,
T = { τ 1 , τ 2 , , τ w 1 } ,
S = { s 1 , s 2 , , s v , s v + 1 } ,
( i = 1 w 1 τ i ) + ( i = 1 v + 1 s i ) = F .
E T = { ( i = k l τ i ) , ( F i = k l τ i ) | 1 k l w 1 } ,
E S = { ( i = k l s i ) | 1 k l v + 1 } ,
E S T = { ( i = k w 1 τ i ) + ( i = 1 l s i ) | 1 k , l v } .
s 1 = s 2 = = s v = s v + 1 = s .
E S = { k s | 1 k v + 1 } ,
E S T = { ( i = k w 1 τ i ) + l s | 1 k , l v } .
E S 1 = { k s | 1 k v } .
( i = k w 1 τ i ) + l s = j s i = k w 1 τ i = ( j l ) s ,
( i = k w 1 τ i ) + l s = ( i = j w 1 τ i ) + m s i = k j 1 τ i = ( m l ) s ,
( i = 1 w 1 τ i ) = F s ( v + 1 ) = ( w 1 ) 2 + ( v + 1 ) ( w s ) .
n ( E S T + E T + E S 1 ) = n ( E S T ) + n ( E T ) + n ( E S 1 ) .
n ( E S T + E T + E S 1 ) = v ( w 1 ) + w ( w 1 ) + v = w ( w + v 1 ) = F 1 .
x i E T x i + x i E S 1 x i + x i E S T x i = 1 + 2 + + ( F 1 ) = F ( F 1 ) 2 .
x i E T x i = k , l = 1 w 1 ( j = k l τ j ) + k , l = 1 w 1 ( F j = k l τ j ) = w ( w 1 ) 2 F ,
x i E S 1 x i = k = 1 v ( j = 1 k s j ) = j = 1 v ( v j + 1 ) s j ,
x i E S T x i = k = 1 v l = 1 w 1 ( j = l w 1 τ j + j = 1 k s j ) = v j = l w 1 j τ j + ( w 1 ) j = l v ( v j + 1 ) s j .
w ( w 1 ) 2 F + v j = 1 w 1 j τ j + w j = 1 v ( v j + 1 ) s j = F ( F 1 ) 2 ,
j = 1 w 1 j τ j + s w ( v + 1 ) 2 = w F 2 .
2 j = 1 w 2 j τ j + 1 = ( w 2 ) [ ( w 1 ) 2 + ( v + 1 ) ( w s ) ] .
w = 2 τ 1 = 1 + ( v + 1 ) ( 2 s ) τ 1 = { 1 ; s = 2 v + 2 ; s = 1 } .
s = 1 : { A j = { j , j + F + 1 2 } ( mod F ) B j = { j , j + F + 1 2 , j + F + 3 2 , , j + F 1 } ( mod F ) } ,
s = 2 : { A j = { j , j + 1 } ( mod F ) B j = { j , j + 1 , j + 3 , j + 5 , , j + F 2 } ( mod F ) } ,
w = 3 { τ 1 + τ 2 = 4 + ( v + 1 ) ( 3 s ) 2 τ 2 = 4 + ( v + 1 ) ( 3 s ) } τ 1 = τ 2 ,
w = 4 { τ 1 + τ 2 + τ 3 = 9 + ( v + 1 ) ( 4 s ) 2 ( τ 2 + 2 τ 3 ) = 2 [ 9 + ( v + 1 ) ( 4 s ) ] } τ 2 + 2 τ 3 = τ 1 + τ 2 + τ 3 τ 1 = τ 3 .
f X ( x | b ) = m = 0 N 1 f X ( x | m , b ) P ( m ) ,
P ( m ) = ( N 1 m ) ( 1 2 ) N 1 .
f X ( x | m , b = 1 ) = j = 0 m + 1 P 1 ( n = j | m ) f X ( x | n = j , b = 1 ) ,
f X ( x | m , b = 0 ) = j = 0 m 1 P 0 ( n = j | m ) f X ( x | n = j , b = 0 ) ,
f 1 + f 2 + + f m + 1 = F .
f k n + 1 + f k n + 2 + + f k m + 1 = F n
u 1 + u 2 + + u m n + 1 = F m 1 .
P 1 ( n | m ) = ( m + 1 n ) × [ Number of Solutions of Eq. ( 40 ) ] Number of Solutions of Eq. ( 35 ) .
P 1 ( n | m ) = ( m + 1 n ) × ( F m 2 m n ) ( F 1 m ) .
f X ( x | b = 1 ) = ( N 1 ) ! ( F 1 ) ! ( 1 2 ) N 1 × m = 0 N 1 j = 0 m + 1 ( m + 1 j ) ( F m 2 m j ) × ( F m 1 ) ! ( N m 1 ) ! f X ( x | n = j , b = 1 ) .
r 1 + u 1 + + u m j 1 + r m + 1 = F m + 1 ,
P 0 ( n | m ) = ( m 1 n ) × [ Number of Solutions of Eq. ( 44 ) ] Number of Solutions of Eq. ( 38 ) = ( m 1 n ) × ( F m m n ) ( F 1 m ) .
f X ( x | b = 0 ) = ( N 1 ) ! ( F 1 ) ! ( 1 2 ) N 1 × m = 0 N 1 j = 0 m ( m 1 j ) ( F m m j ) × ( F m 1 ) ! ( N m 1 ) ! f X ( x | n = j , b = 0 ) .
f X ( x | n , b = 1 ) = 1 2 π n σ 0 2 exp [ ( x 2 I 0 ) 2 n σ 0 2 ] ,
f X ( x | n , b = 0 ) = 1 2 π n σ 0 2 exp [ x 2 n σ 0 2 ] ,
σ 0 2 = 2 B e Δ υ ( R P sr F ) 2 ,
I 0 = R P sr F ,
P e = Th f X ( x | n , b = 1 ) d x + Th f X ( x | n , b = 0 ) d x ,
s j = s 1 + i = k j w 1 τ i ; 2 j v + 1 .
i = x y s i = i = n m 1 τ i ,
i = x y s i = a n a m = i = n w 1 τ i + i = 1 l s i ,
s 2 = s 1 + i = n w 1 τ i .
s j = s 1 + i = h w 1 τ i
i = 2 k s i = i = n w 1 τ i + i = 1 l s i .
i = l + 1 k + 1 s i = i = n w 1 τ i + s 1 .
s l + 1 = s 1 + i = u w 1 τ i
i = l + 2 k + 1 s i + ( s 1 + i = u w 1 τ i ) = i = n w 1 τ i + s 1 .
i = l + 2 k + 1 s i = i = n u 1 τ i .
s k + 1 = i = n w 1 τ i + s 1 .
s j = s v + 1 + i = 1 l j τ i , 1 j v .
s v + 1 = s 1 + i = k j w 1 τ i ,
s 1 = s v + 1 + i = 1 l j τ i ,
s 1 = s v + 1 .
s v + 1 + i = 1 l j τ i = s 1 + i = k j w 1 τ i ,
i = 1 l j τ i = i = k j w 1 τ i .
s j = s 1 = s v + 1 , 2 j v .