Abstract

Algebraic optical codes with large cardinality and unique tree structures of multiple levels of subsets of codewords for adjustable code performance and cardinality have recently been proposed. As shown in this paper, these characteristics support new network architecture and applications for rapid code switching and physical-layer security in optical code-division multiple access networks. In addition, a new “translate” method of converting “additive” error-correction codes (ECCs) into this kind of optical codes is investigated and demonstrated with four families of Reed–Solomon codes. With rich families of ECCs, our method enhances the collections of optical codes. The performances of these “tree-structured” optical codes are algebraically analyzed and verified, for the first time, using the weight distribution of ECCs.

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  1. F. R. K. Chung, J. A. Salehi, and V. K. Wei, “Optical orthogonal codes: Design, analysis, and applications,” IEEE Trans. Inf. Theory, vol. 35. no. 3, pp. 595–604, 1989.
  2. W. C. Kwong, P. A. Perrier, and P. R. Prucnal, “Performance comparison of asynchronous and synchronous code-division multiple-access techniques for fiber-optic local area networks,” IEEE Trans. Commun., vol. 39, no. 11, pp. 1625–1634,  1991.
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  9. W. C. Kwong and G.-C. Yang, “Multiple-length, multiple-wavelength optical orthogonal codes for optical CDMA systems supporting multirate, multimedia services,” IEEE J. Sel. Areas Commun., vol. 22, no. 9, pp. 1640–1647,  2004.
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  13. O. Moreno, R. Omrani, P. V. Kumar, and H.-F. Lu, “A generalized Bose-Chowla family of optical orthogonal codes and distinct difference sets,” IEEE Trans. Inf. Theory, vol. 53, no. 5, pp. 1907–1910,  2007.
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  30. R. M. Roth and G. Seroussi, “On cyclic MDS codes of length $q$ over GF($q$),” IEEE Trans. Inf. Theory, vol. 32, no. 2, pp. 284–285,  1986.
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2010

Z. Wang, J. Chang, and P. R. Prucnal, “Theoretical analysis and experimental investigation on the confidentiality of 2-D incoherent optical CDMA system,” J. Lightw. Technol., vol. 28, no. 12, pp. 1761–1769, , 2010.

2009

Z. Wang, Y.-K. Huang, Y. Deng, J. Chang, and P. R. Prucnal, “Optical encryption with OCDMA code swapping using all-optical XOR logic gate,” IEEE Photon. Technol. Lett., vol. 21, no. 7, pp. 411–413, 1, 2009.

2008

S. Etemad, A. Agarwal, T. Banwell, G. Di Crescenzo, J. Jackel, R. Menendez, and P. Toliver, “An overlay photonic layer security approach scalable to 100 Gb/s,” IEEE Commun. Mag., vol. 46, no. 8, pp. 32–39, 2008.

2004

S. Lin and D. J. Costello, Error Control Coding: Fundamentals and Applications, 2nd ed. Upper Saddle River, NJ, USA: Pearson Education, 2004.

1989

F. R. K. Chung, J. A. Salehi, and V. K. Wei, “Optical orthogonal codes: Design, analysis, and applications,” IEEE Trans. Inf. Theory, vol. 35. no. 3, pp. 595–604, 1989.

1960

R. C. Bose and D. K. Ray Chaudhuri, “On a class of error correcting binary group codes,” Inform. Control, vol. 3, pp. 68–79, 1960.

Agarwal, A.

S. Etemad, A. Agarwal, T. Banwell, G. Di Crescenzo, J. Jackel, R. Menendez, and P. Toliver, “An overlay photonic layer security approach scalable to 100 Gb/s,” IEEE Commun. Mag., vol. 46, no. 8, pp. 32–39, 2008.

Andonovic, I.

L. Tancevski and I. Andonovic, “Hybrid wavelength hopping/time spreading schemes for use in massive optical networks with increased security,” J. Lightw. Technol., vol. 14, no. 12, pp. 2636–2647,  1996.

Araki, S.

K.-I. Kitayama, M. Sasaki, S. Araki, M. Tsubokawa, A. Tomita, K. Inoue, K. Harasawa, Y. Nagasako, and A. Takada, “Security in photonic networks: Threats and security enhancement,” J. Lightw. Technol., vol. 29, no. 21, pp. 3210–3219,  2011.

Baby, V.

W. C. Kwong, G.-C. Yang, V. Baby, C.-S. Brès, and P. R. Prucnal, “Multiple-wavelength optical orthogonal codes under prime-sequence permutations for optical CDMA,” IEEE Trans. Commun., vol. 53, no. 1, pp. 117–123,  2005.

Banwell, T.

S. Etemad, A. Agarwal, T. Banwell, G. Di Crescenzo, J. Jackel, R. Menendez, and P. Toliver, “An overlay photonic layer security approach scalable to 100 Gb/s,” IEEE Commun. Mag., vol. 46, no. 8, pp. 32–39, 2008.

Bhambhani, P.

R. Omrani, G. Garg, P. V. Kumar, P. Elia, and P. Bhambhani, “Large families of asymptotically optimal two-dimensional optical orthogonal codes,” IEEE Trans. Inf. Theory, vol. 58, no. 2, pp. 1163–1185,  2012.

Bose, R. C.

R. C. Bose and D. K. Ray Chaudhuri, “On a class of error correcting binary group codes,” Inform. Control, vol. 3, pp. 68–79, 1960.

Brès, C.-S.

W. C. Kwong, G.-C. Yang, V. Baby, C.-S. Brès, and P. R. Prucnal, “Multiple-wavelength optical orthogonal codes under prime-sequence permutations for optical CDMA,” IEEE Trans. Commun., vol. 53, no. 1, pp. 117–123,  2005.

Chang, C.-Y.

Y.-C. Lin, G.-C. Yang, C.-Y. Chang, and W. C. Kwong, “Construction of optimal 2D optical codes using $(n,w,2,2)$ optical orthogonal codes,” IEEE Trans. Commun., vol. 59, no. 1, pp. 194–200,  2011.

C.-C. Sun, G.-C. Yang, C.-P. Tu, C.-Y. Chang, and W. C. Kwong, “Extended multilevel prime codes for optical CDMA,” IEEE Trans. Commun., vol. 58, no. 5, pp. 1344–1350,  2010.

C.-H. Hsieh, G.-C. Yang, C.-Y. Chang, and W. C. Kwong, “Multilevel prime codes for optical CDMA systems,” J. Opt. Commun. Netw., vol. 1, no. 7, pp. 600–607,  2009.

J.-H. Tien, G.-C. Yang, C.-Y. Chang, and W. C. Kwong, “Design and analysis of 2-D codes with the maximum cross-correlation value of two for optical CDMA,” J. Lightw. Technol., vol. 26, no. 22, pp. 3632–3639,  2008.

C.-Y. Chang, G.-C. Yang, and W.C. Kwong, “Wavelength-time codes with maximum cross-correlation function of two for multicode-keying optical CDMA,” J. Lightw. Technol., vol. 24, no. 3, pp. 1093–1100,  2006.

Chang, J.

Z. Wang, J. Chang, and P. R. Prucnal, “Theoretical analysis and experimental investigation on the confidentiality of 2-D incoherent optical CDMA system,” J. Lightw. Technol., vol. 28, no. 12, pp. 1761–1769, , 2010.

Z. Wang, Y.-K. Huang, Y. Deng, J. Chang, and P. R. Prucnal, “Optical encryption with OCDMA code swapping using all-optical XOR logic gate,” IEEE Photon. Technol. Lett., vol. 21, no. 7, pp. 411–413, 1, 2009.

Chaudhuri, D. K. Ray

R. C. Bose and D. K. Ray Chaudhuri, “On a class of error correcting binary group codes,” Inform. Control, vol. 3, pp. 68–79, 1960.

Chen, H.

Y.-F. Li, G.-C. Yang, H. Chen, and W.C. Kwong, “Extended Reed-Solomon codes for optical CDMA,” IEEE Trans. Commun., vol. 61, no. 6, pp. 2498–2507,  2013.

Chung, F. R. K.

F. R. K. Chung, J. A. Salehi, and V. K. Wei, “Optical orthogonal codes: Design, analysis, and applications,” IEEE Trans. Inf. Theory, vol. 35. no. 3, pp. 595–604, 1989.

Costello, D. J.

S. Lin and D. J. Costello, Error Control Coding: Fundamentals and Applications, 2nd ed. Upper Saddle River, NJ, USA: Pearson Education, 2004.

Crescenzo, G. Di

S. Etemad, A. Agarwal, T. Banwell, G. Di Crescenzo, J. Jackel, R. Menendez, and P. Toliver, “An overlay photonic layer security approach scalable to 100 Gb/s,” IEEE Commun. Mag., vol. 46, no. 8, pp. 32–39, 2008.

Deng, Y.

Z. Wang, Y.-K. Huang, Y. Deng, J. Chang, and P. R. Prucnal, “Optical encryption with OCDMA code swapping using all-optical XOR logic gate,” IEEE Photon. Technol. Lett., vol. 21, no. 7, pp. 411–413, 1, 2009.

Elia, P.

R. Omrani, G. Garg, P. V. Kumar, P. Elia, and P. Bhambhani, “Large families of asymptotically optimal two-dimensional optical orthogonal codes,” IEEE Trans. Inf. Theory, vol. 58, no. 2, pp. 1163–1185,  2012.

Etemad, S.

S. Etemad, A. Agarwal, T. Banwell, G. Di Crescenzo, J. Jackel, R. Menendez, and P. Toliver, “An overlay photonic layer security approach scalable to 100 Gb/s,” IEEE Commun. Mag., vol. 46, no. 8, pp. 32–39, 2008.

Fuja, T.

G.-C. Yang and T. Fuja, “Optical orthogonal codes with unequal auto- and cross-correlation constraints,” IEEE Trans. Inf. Theory, vol. 41, no. 1, pp. 96–106,  1995.

Fuji-Hara, R.

R. Fuji-Hara and Y. Miao, “Optical orthogonal codes: Their bounds and new optimal constructions,” IEEE Trans. Inf. Theory, vol. 46, no. 7, pp. 2396–2406,  2000.

Garg, G.

R. Omrani, G. Garg, P. V. Kumar, P. Elia, and P. Bhambhani, “Large families of asymptotically optimal two-dimensional optical orthogonal codes,” IEEE Trans. Inf. Theory, vol. 58, no. 2, pp. 1163–1185,  2012.

Györfi, L.

Q. A. Nguyen, L. Györfi, and J. L. Massey, “Constructions of binary constant-weight cyclic codes and cyclically permutable codes,” IEEE Trans. Inf. Theory, vol. 38, no. 3, pp. 940–949,  1992.

Harasawa, K.

K.-I. Kitayama, M. Sasaki, S. Araki, M. Tsubokawa, A. Tomita, K. Inoue, K. Harasawa, Y. Nagasako, and A. Takada, “Security in photonic networks: Threats and security enhancement,” J. Lightw. Technol., vol. 29, no. 21, pp. 3210–3219,  2011.

Hsieh, C.-H.

Huang, Y.-K.

Z. Wang, Y.-K. Huang, Y. Deng, J. Chang, and P. R. Prucnal, “Optical encryption with OCDMA code swapping using all-optical XOR logic gate,” IEEE Photon. Technol. Lett., vol. 21, no. 7, pp. 411–413, 1, 2009.

Inoue, K.

K.-I. Kitayama, M. Sasaki, S. Araki, M. Tsubokawa, A. Tomita, K. Inoue, K. Harasawa, Y. Nagasako, and A. Takada, “Security in photonic networks: Threats and security enhancement,” J. Lightw. Technol., vol. 29, no. 21, pp. 3210–3219,  2011.

Jackel, J.

S. Etemad, A. Agarwal, T. Banwell, G. Di Crescenzo, J. Jackel, R. Menendez, and P. Toliver, “An overlay photonic layer security approach scalable to 100 Gb/s,” IEEE Commun. Mag., vol. 46, no. 8, pp. 32–39, 2008.

Kitayama, K.-I.

K.-I. Kitayama, M. Sasaki, S. Araki, M. Tsubokawa, A. Tomita, K. Inoue, K. Harasawa, Y. Nagasako, and A. Takada, “Security in photonic networks: Threats and security enhancement,” J. Lightw. Technol., vol. 29, no. 21, pp. 3210–3219,  2011.

Kumar, P. V.

R. Omrani, G. Garg, P. V. Kumar, P. Elia, and P. Bhambhani, “Large families of asymptotically optimal two-dimensional optical orthogonal codes,” IEEE Trans. Inf. Theory, vol. 58, no. 2, pp. 1163–1185,  2012.

O. Moreno, R. Omrani, P. V. Kumar, and H.-F. Lu, “A generalized Bose-Chowla family of optical orthogonal codes and distinct difference sets,” IEEE Trans. Inf. Theory, vol. 53, no. 5, pp. 1907–1910,  2007.

Kwong, W. C.

Y.-C. Lin, G.-C. Yang, C.-Y. Chang, and W. C. Kwong, “Construction of optimal 2D optical codes using $(n,w,2,2)$ optical orthogonal codes,” IEEE Trans. Commun., vol. 59, no. 1, pp. 194–200,  2011.

J.-H. Tien, G.-C. Yang, C.-Y. Chang, and W. C. Kwong, “Design and analysis of 2-D codes with the maximum cross-correlation value of two for optical CDMA,” J. Lightw. Technol., vol. 26, no. 22, pp. 3632–3639,  2008.

E. Narimanov, W. C. Kwong, G.-C. Yang, and P. R. Prucnal, “Shifted carrier-hopping prime codes for multicode keying in wavelength-time O-CDMA,” IEEE Trans. Commun., vol. 53, no. 12, pp. 2150–2156,  2005.

W. C. Kwong, G.-C. Yang, V. Baby, C.-S. Brès, and P. R. Prucnal, “Multiple-wavelength optical orthogonal codes under prime-sequence permutations for optical CDMA,” IEEE Trans. Commun., vol. 53, no. 1, pp. 117–123,  2005.

W. C. Kwong and G.-C. Yang, “Multiple-length, multiple-wavelength optical orthogonal codes for optical CDMA systems supporting multirate, multimedia services,” IEEE J. Sel. Areas Commun., vol. 22, no. 9, pp. 1640–1647,  2004.

W. C. Kwong and G.-C. Yang, “Design of multilength optical orthogonal codes for optical CDMA multimedia networks,” IEEE Trans. Commun., vol. 50, no. 8, pp. 1258–1265,  2002.

W. C. Kwong, P. A. Perrier, and P. R. Prucnal, “Performance comparison of asynchronous and synchronous code-division multiple-access techniques for fiber-optic local area networks,” IEEE Trans. Commun., vol. 39, no. 11, pp. 1625–1634,  1991.

G.-C. Yang and W. C. Kwong, Prime Codes with Applications to CDMA Optical and Wireless Networks. Norwood, MA, USA: Artech House, 2002.

W. C. Kwong and G.-C. Yang, Optical Coding Theory with Prime. New York, NY, USA: CRC Press, 2013.

Kwong, W. C.

C.-C. Sun, G.-C. Yang, C.-P. Tu, C.-Y. Chang, and W. C. Kwong, “Extended multilevel prime codes for optical CDMA,” IEEE Trans. Commun., vol. 58, no. 5, pp. 1344–1350,  2010.

C.-H. Hsieh, G.-C. Yang, C.-Y. Chang, and W. C. Kwong, “Multilevel prime codes for optical CDMA systems,” J. Opt. Commun. Netw., vol. 1, no. 7, pp. 600–607,  2009.

Kwong, W.C.

Y.-F. Li, G.-C. Yang, H. Chen, and W.C. Kwong, “Extended Reed-Solomon codes for optical CDMA,” IEEE Trans. Commun., vol. 61, no. 6, pp. 2498–2507,  2013.

C.-Y. Chang, G.-C. Yang, and W.C. Kwong, “Wavelength-time codes with maximum cross-correlation function of two for multicode-keying optical CDMA,” J. Lightw. Technol., vol. 24, no. 3, pp. 1093–1100,  2006.

G.-C. Yang and W.C. Kwong, “Performance comparison of multiwavelength CDMA and WDMA + CDMA for fiber-optic networks,” IEEE Trans. Commun., vol. 45, no. 11, pp. 1426–1434,  1997.

Li, Y.-F.

Y.-F. Li, G.-C. Yang, H. Chen, and W.C. Kwong, “Extended Reed-Solomon codes for optical CDMA,” IEEE Trans. Commun., vol. 61, no. 6, pp. 2498–2507,  2013.

Lin, S.

S. Lin and D. J. Costello, Error Control Coding: Fundamentals and Applications, 2nd ed. Upper Saddle River, NJ, USA: Pearson Education, 2004.

Lin, Y.-C.

Y.-C. Lin, G.-C. Yang, C.-Y. Chang, and W. C. Kwong, “Construction of optimal 2D optical codes using $(n,w,2,2)$ optical orthogonal codes,” IEEE Trans. Commun., vol. 59, no. 1, pp. 194–200,  2011.

Lu, H.-F.

O. Moreno, R. Omrani, P. V. Kumar, and H.-F. Lu, “A generalized Bose-Chowla family of optical orthogonal codes and distinct difference sets,” IEEE Trans. Inf. Theory, vol. 53, no. 5, pp. 1907–1910,  2007.

Macwilliams, F. J.

F. J. Macwilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes. Amsterdam, The Netherlands: North Holland, 1977.

Massey, J. L.

Q. A. Nguyen, L. Györfi, and J. L. Massey, “Constructions of binary constant-weight cyclic codes and cyclically permutable codes,” IEEE Trans. Inf. Theory, vol. 38, no. 3, pp. 940–949,  1992.

Menendez, R.

S. Etemad, A. Agarwal, T. Banwell, G. Di Crescenzo, J. Jackel, R. Menendez, and P. Toliver, “An overlay photonic layer security approach scalable to 100 Gb/s,” IEEE Commun. Mag., vol. 46, no. 8, pp. 32–39, 2008.

Miao, Y.

R. Fuji-Hara and Y. Miao, “Optical orthogonal codes: Their bounds and new optimal constructions,” IEEE Trans. Inf. Theory, vol. 46, no. 7, pp. 2396–2406,  2000.

Moreno, O.

O. Moreno, R. Omrani, P. V. Kumar, and H.-F. Lu, “A generalized Bose-Chowla family of optical orthogonal codes and distinct difference sets,” IEEE Trans. Inf. Theory, vol. 53, no. 5, pp. 1907–1910,  2007.

Nagasako, Y.

K.-I. Kitayama, M. Sasaki, S. Araki, M. Tsubokawa, A. Tomita, K. Inoue, K. Harasawa, Y. Nagasako, and A. Takada, “Security in photonic networks: Threats and security enhancement,” J. Lightw. Technol., vol. 29, no. 21, pp. 3210–3219,  2011.

Narimanov, E.

E. Narimanov, W. C. Kwong, G.-C. Yang, and P. R. Prucnal, “Shifted carrier-hopping prime codes for multicode keying in wavelength-time O-CDMA,” IEEE Trans. Commun., vol. 53, no. 12, pp. 2150–2156,  2005.

Nguyen, Q. A.

Q. A. Nguyen, L. Györfi, and J. L. Massey, “Constructions of binary constant-weight cyclic codes and cyclically permutable codes,” IEEE Trans. Inf. Theory, vol. 38, no. 3, pp. 940–949,  1992.

Omrani, R.

R. Omrani, G. Garg, P. V. Kumar, P. Elia, and P. Bhambhani, “Large families of asymptotically optimal two-dimensional optical orthogonal codes,” IEEE Trans. Inf. Theory, vol. 58, no. 2, pp. 1163–1185,  2012.

O. Moreno, R. Omrani, P. V. Kumar, and H.-F. Lu, “A generalized Bose-Chowla family of optical orthogonal codes and distinct difference sets,” IEEE Trans. Inf. Theory, vol. 53, no. 5, pp. 1907–1910,  2007.

Perrier, P. A.

W. C. Kwong, P. A. Perrier, and P. R. Prucnal, “Performance comparison of asynchronous and synchronous code-division multiple-access techniques for fiber-optic local area networks,” IEEE Trans. Commun., vol. 39, no. 11, pp. 1625–1634,  1991.

Prucnal, P. R.

Z. Wang, J. Chang, and P. R. Prucnal, “Theoretical analysis and experimental investigation on the confidentiality of 2-D incoherent optical CDMA system,” J. Lightw. Technol., vol. 28, no. 12, pp. 1761–1769, , 2010.

Z. Wang, Y.-K. Huang, Y. Deng, J. Chang, and P. R. Prucnal, “Optical encryption with OCDMA code swapping using all-optical XOR logic gate,” IEEE Photon. Technol. Lett., vol. 21, no. 7, pp. 411–413, 1, 2009.

E. Narimanov, W. C. Kwong, G.-C. Yang, and P. R. Prucnal, “Shifted carrier-hopping prime codes for multicode keying in wavelength-time O-CDMA,” IEEE Trans. Commun., vol. 53, no. 12, pp. 2150–2156,  2005.

W. C. Kwong, G.-C. Yang, V. Baby, C.-S. Brès, and P. R. Prucnal, “Multiple-wavelength optical orthogonal codes under prime-sequence permutations for optical CDMA,” IEEE Trans. Commun., vol. 53, no. 1, pp. 117–123,  2005.

W. C. Kwong, P. A. Perrier, and P. R. Prucnal, “Performance comparison of asynchronous and synchronous code-division multiple-access techniques for fiber-optic local area networks,” IEEE Trans. Commun., vol. 39, no. 11, pp. 1625–1634,  1991.

Reed, I. S.

I. S. Reed, “$k$-th order near-orthogonal codes,” IEEE Trans. Inf. Theory, vol. 17, no. 1, pp. 116–117,  1971.

Rocha, V. C.

V. C. Rocha, Jr, “Maximum distance separable multilevel codes,” IEEE Trans. Inf. Theory, vol. 30, no. 3, pp. 547–548,  1984.

Roth, R. M.

R. M. Roth and G. Seroussi, “On cyclic MDS codes of length $q$ over GF($q$),” IEEE Trans. Inf. Theory, vol. 32, no. 2, pp. 284–285,  1986.

Salehi, J. A.

F. R. K. Chung, J. A. Salehi, and V. K. Wei, “Optical orthogonal codes: Design, analysis, and applications,” IEEE Trans. Inf. Theory, vol. 35. no. 3, pp. 595–604, 1989.

Sasaki, M.

K.-I. Kitayama, M. Sasaki, S. Araki, M. Tsubokawa, A. Tomita, K. Inoue, K. Harasawa, Y. Nagasako, and A. Takada, “Security in photonic networks: Threats and security enhancement,” J. Lightw. Technol., vol. 29, no. 21, pp. 3210–3219,  2011.

Seroussi, G.

R. M. Roth and G. Seroussi, “On cyclic MDS codes of length $q$ over GF($q$),” IEEE Trans. Inf. Theory, vol. 32, no. 2, pp. 284–285,  1986.

Shake, T. H.

T. H. Shake, “Security performance of optical CDMA against eavesdropping,” J. Lightw. Technol., vol. 23, no. 2, pp. 655–670,  2005.

Sloane, N. J. A.

F. J. Macwilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes. Amsterdam, The Netherlands: North Holland, 1977.

Sun, C.-C.

C.-C. Sun, G.-C. Yang, C.-P. Tu, C.-Y. Chang, and W. C. Kwong, “Extended multilevel prime codes for optical CDMA,” IEEE Trans. Commun., vol. 58, no. 5, pp. 1344–1350,  2010.

Takada, A.

K.-I. Kitayama, M. Sasaki, S. Araki, M. Tsubokawa, A. Tomita, K. Inoue, K. Harasawa, Y. Nagasako, and A. Takada, “Security in photonic networks: Threats and security enhancement,” J. Lightw. Technol., vol. 29, no. 21, pp. 3210–3219,  2011.

Tancevski, L.

L. Tancevski and I. Andonovic, “Hybrid wavelength hopping/time spreading schemes for use in massive optical networks with increased security,” J. Lightw. Technol., vol. 14, no. 12, pp. 2636–2647,  1996.

Tien, J.-H.

J.-H. Tien, G.-C. Yang, C.-Y. Chang, and W. C. Kwong, “Design and analysis of 2-D codes with the maximum cross-correlation value of two for optical CDMA,” J. Lightw. Technol., vol. 26, no. 22, pp. 3632–3639,  2008.

Toliver, P.

S. Etemad, A. Agarwal, T. Banwell, G. Di Crescenzo, J. Jackel, R. Menendez, and P. Toliver, “An overlay photonic layer security approach scalable to 100 Gb/s,” IEEE Commun. Mag., vol. 46, no. 8, pp. 32–39, 2008.

Tomita, A.

K.-I. Kitayama, M. Sasaki, S. Araki, M. Tsubokawa, A. Tomita, K. Inoue, K. Harasawa, Y. Nagasako, and A. Takada, “Security in photonic networks: Threats and security enhancement,” J. Lightw. Technol., vol. 29, no. 21, pp. 3210–3219,  2011.

Tsubokawa, M.

K.-I. Kitayama, M. Sasaki, S. Araki, M. Tsubokawa, A. Tomita, K. Inoue, K. Harasawa, Y. Nagasako, and A. Takada, “Security in photonic networks: Threats and security enhancement,” J. Lightw. Technol., vol. 29, no. 21, pp. 3210–3219,  2011.

Tu, C.-P.

C.-C. Sun, G.-C. Yang, C.-P. Tu, C.-Y. Chang, and W. C. Kwong, “Extended multilevel prime codes for optical CDMA,” IEEE Trans. Commun., vol. 58, no. 5, pp. 1344–1350,  2010.

Wang, Z.

Z. Wang, J. Chang, and P. R. Prucnal, “Theoretical analysis and experimental investigation on the confidentiality of 2-D incoherent optical CDMA system,” J. Lightw. Technol., vol. 28, no. 12, pp. 1761–1769, , 2010.

Z. Wang, Y.-K. Huang, Y. Deng, J. Chang, and P. R. Prucnal, “Optical encryption with OCDMA code swapping using all-optical XOR logic gate,” IEEE Photon. Technol. Lett., vol. 21, no. 7, pp. 411–413, 1, 2009.

Wei, V. K.

F. R. K. Chung, J. A. Salehi, and V. K. Wei, “Optical orthogonal codes: Design, analysis, and applications,” IEEE Trans. Inf. Theory, vol. 35. no. 3, pp. 595–604, 1989.

Wicker, S. B.

S. B. Wicker, Error Control Systems for Digital Communication and Storage. Upper Saddle River, NJ, USA: Prentice-Hall, 1994.

Yang, G.-C.

Y.-F. Li, G.-C. Yang, H. Chen, and W.C. Kwong, “Extended Reed-Solomon codes for optical CDMA,” IEEE Trans. Commun., vol. 61, no. 6, pp. 2498–2507,  2013.

Y.-C. Lin, G.-C. Yang, C.-Y. Chang, and W. C. Kwong, “Construction of optimal 2D optical codes using $(n,w,2,2)$ optical orthogonal codes,” IEEE Trans. Commun., vol. 59, no. 1, pp. 194–200,  2011.

C.-C. Sun, G.-C. Yang, C.-P. Tu, C.-Y. Chang, and W. C. Kwong, “Extended multilevel prime codes for optical CDMA,” IEEE Trans. Commun., vol. 58, no. 5, pp. 1344–1350,  2010.

C.-H. Hsieh, G.-C. Yang, C.-Y. Chang, and W. C. Kwong, “Multilevel prime codes for optical CDMA systems,” J. Opt. Commun. Netw., vol. 1, no. 7, pp. 600–607,  2009.

J.-H. Tien, G.-C. Yang, C.-Y. Chang, and W. C. Kwong, “Design and analysis of 2-D codes with the maximum cross-correlation value of two for optical CDMA,” J. Lightw. Technol., vol. 26, no. 22, pp. 3632–3639,  2008.

C.-Y. Chang, G.-C. Yang, and W.C. Kwong, “Wavelength-time codes with maximum cross-correlation function of two for multicode-keying optical CDMA,” J. Lightw. Technol., vol. 24, no. 3, pp. 1093–1100,  2006.

E. Narimanov, W. C. Kwong, G.-C. Yang, and P. R. Prucnal, “Shifted carrier-hopping prime codes for multicode keying in wavelength-time O-CDMA,” IEEE Trans. Commun., vol. 53, no. 12, pp. 2150–2156,  2005.

W. C. Kwong, G.-C. Yang, V. Baby, C.-S. Brès, and P. R. Prucnal, “Multiple-wavelength optical orthogonal codes under prime-sequence permutations for optical CDMA,” IEEE Trans. Commun., vol. 53, no. 1, pp. 117–123,  2005.

W. C. Kwong and G.-C. Yang, “Multiple-length, multiple-wavelength optical orthogonal codes for optical CDMA systems supporting multirate, multimedia services,” IEEE J. Sel. Areas Commun., vol. 22, no. 9, pp. 1640–1647,  2004.

W. C. Kwong and G.-C. Yang, “Design of multilength optical orthogonal codes for optical CDMA multimedia networks,” IEEE Trans. Commun., vol. 50, no. 8, pp. 1258–1265,  2002.

G.-C. Yang and W.C. Kwong, “Performance comparison of multiwavelength CDMA and WDMA + CDMA for fiber-optic networks,” IEEE Trans. Commun., vol. 45, no. 11, pp. 1426–1434,  1997.

G.-C. Yang and T. Fuja, “Optical orthogonal codes with unequal auto- and cross-correlation constraints,” IEEE Trans. Inf. Theory, vol. 41, no. 1, pp. 96–106,  1995.

G.-C. Yang and W. C. Kwong, Prime Codes with Applications to CDMA Optical and Wireless Networks. Norwood, MA, USA: Artech House, 2002.

W. C. Kwong and G.-C. Yang, Optical Coding Theory with Prime. New York, NY, USA: CRC Press, 2013.

Error Control Coding: Fundamentals and Applications

S. Lin and D. J. Costello, Error Control Coding: Fundamentals and Applications, 2nd ed. Upper Saddle River, NJ, USA: Pearson Education, 2004.

IEEE Commun. Mag.

S. Etemad, A. Agarwal, T. Banwell, G. Di Crescenzo, J. Jackel, R. Menendez, and P. Toliver, “An overlay photonic layer security approach scalable to 100 Gb/s,” IEEE Commun. Mag., vol. 46, no. 8, pp. 32–39, 2008.

IEEE J. Sel. Areas Commun.

W. C. Kwong and G.-C. Yang, “Multiple-length, multiple-wavelength optical orthogonal codes for optical CDMA systems supporting multirate, multimedia services,” IEEE J. Sel. Areas Commun., vol. 22, no. 9, pp. 1640–1647,  2004.

IEEE Photon. Technol. Lett.

Z. Wang, Y.-K. Huang, Y. Deng, J. Chang, and P. R. Prucnal, “Optical encryption with OCDMA code swapping using all-optical XOR logic gate,” IEEE Photon. Technol. Lett., vol. 21, no. 7, pp. 411–413, 1, 2009.

IEEE Trans. Commun.

C.-C. Sun, G.-C. Yang, C.-P. Tu, C.-Y. Chang, and W. C. Kwong, “Extended multilevel prime codes for optical CDMA,” IEEE Trans. Commun., vol. 58, no. 5, pp. 1344–1350,  2010.

Y.-F. Li, G.-C. Yang, H. Chen, and W.C. Kwong, “Extended Reed-Solomon codes for optical CDMA,” IEEE Trans. Commun., vol. 61, no. 6, pp. 2498–2507,  2013.

W. C. Kwong, G.-C. Yang, V. Baby, C.-S. Brès, and P. R. Prucnal, “Multiple-wavelength optical orthogonal codes under prime-sequence permutations for optical CDMA,” IEEE Trans. Commun., vol. 53, no. 1, pp. 117–123,  2005.

E. Narimanov, W. C. Kwong, G.-C. Yang, and P. R. Prucnal, “Shifted carrier-hopping prime codes for multicode keying in wavelength-time O-CDMA,” IEEE Trans. Commun., vol. 53, no. 12, pp. 2150–2156,  2005.

W. C. Kwong, P. A. Perrier, and P. R. Prucnal, “Performance comparison of asynchronous and synchronous code-division multiple-access techniques for fiber-optic local area networks,” IEEE Trans. Commun., vol. 39, no. 11, pp. 1625–1634,  1991.

G.-C. Yang and W.C. Kwong, “Performance comparison of multiwavelength CDMA and WDMA + CDMA for fiber-optic networks,” IEEE Trans. Commun., vol. 45, no. 11, pp. 1426–1434,  1997.

W. C. Kwong and G.-C. Yang, “Design of multilength optical orthogonal codes for optical CDMA multimedia networks,” IEEE Trans. Commun., vol. 50, no. 8, pp. 1258–1265,  2002.

Y.-C. Lin, G.-C. Yang, C.-Y. Chang, and W. C. Kwong, “Construction of optimal 2D optical codes using $(n,w,2,2)$ optical orthogonal codes,” IEEE Trans. Commun., vol. 59, no. 1, pp. 194–200,  2011.

IEEE Trans. Inf. Theory

R. Omrani, G. Garg, P. V. Kumar, P. Elia, and P. Bhambhani, “Large families of asymptotically optimal two-dimensional optical orthogonal codes,” IEEE Trans. Inf. Theory, vol. 58, no. 2, pp. 1163–1185,  2012.

F. R. K. Chung, J. A. Salehi, and V. K. Wei, “Optical orthogonal codes: Design, analysis, and applications,” IEEE Trans. Inf. Theory, vol. 35. no. 3, pp. 595–604, 1989.

O. Moreno, R. Omrani, P. V. Kumar, and H.-F. Lu, “A generalized Bose-Chowla family of optical orthogonal codes and distinct difference sets,” IEEE Trans. Inf. Theory, vol. 53, no. 5, pp. 1907–1910,  2007.

R. Fuji-Hara and Y. Miao, “Optical orthogonal codes: Their bounds and new optimal constructions,” IEEE Trans. Inf. Theory, vol. 46, no. 7, pp. 2396–2406,  2000.

G.-C. Yang and T. Fuja, “Optical orthogonal codes with unequal auto- and cross-correlation constraints,” IEEE Trans. Inf. Theory, vol. 41, no. 1, pp. 96–106,  1995.

Q. A. Nguyen, L. Györfi, and J. L. Massey, “Constructions of binary constant-weight cyclic codes and cyclically permutable codes,” IEEE Trans. Inf. Theory, vol. 38, no. 3, pp. 940–949,  1992.

I. S. Reed, “$k$-th order near-orthogonal codes,” IEEE Trans. Inf. Theory, vol. 17, no. 1, pp. 116–117,  1971.

V. C. Rocha, Jr, “Maximum distance separable multilevel codes,” IEEE Trans. Inf. Theory, vol. 30, no. 3, pp. 547–548,  1984.

R. M. Roth and G. Seroussi, “On cyclic MDS codes of length $q$ over GF($q$),” IEEE Trans. Inf. Theory, vol. 32, no. 2, pp. 284–285,  1986.

Inform. Control

R. C. Bose and D. K. Ray Chaudhuri, “On a class of error correcting binary group codes,” Inform. Control, vol. 3, pp. 68–79, 1960.

J. Lightw. Technol.

Z. Wang, J. Chang, and P. R. Prucnal, “Theoretical analysis and experimental investigation on the confidentiality of 2-D incoherent optical CDMA system,” J. Lightw. Technol., vol. 28, no. 12, pp. 1761–1769, , 2010.

K.-I. Kitayama, M. Sasaki, S. Araki, M. Tsubokawa, A. Tomita, K. Inoue, K. Harasawa, Y. Nagasako, and A. Takada, “Security in photonic networks: Threats and security enhancement,” J. Lightw. Technol., vol. 29, no. 21, pp. 3210–3219,  2011.

L. Tancevski and I. Andonovic, “Hybrid wavelength hopping/time spreading schemes for use in massive optical networks with increased security,” J. Lightw. Technol., vol. 14, no. 12, pp. 2636–2647,  1996.

C.-Y. Chang, G.-C. Yang, and W.C. Kwong, “Wavelength-time codes with maximum cross-correlation function of two for multicode-keying optical CDMA,” J. Lightw. Technol., vol. 24, no. 3, pp. 1093–1100,  2006.

J.-H. Tien, G.-C. Yang, C.-Y. Chang, and W. C. Kwong, “Design and analysis of 2-D codes with the maximum cross-correlation value of two for optical CDMA,” J. Lightw. Technol., vol. 26, no. 22, pp. 3632–3639,  2008.

T. H. Shake, “Security performance of optical CDMA against eavesdropping,” J. Lightw. Technol., vol. 23, no. 2, pp. 655–670,  2005.

J. Opt. Commun. Netw.

Other

F. J. Macwilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes. Amsterdam, The Netherlands: North Holland, 1977.

S. B. Wicker, Error Control Systems for Digital Communication and Storage. Upper Saddle River, NJ, USA: Prentice-Hall, 1994.

W. C. Kwong and G.-C. Yang, Optical Coding Theory with Prime. New York, NY, USA: CRC Press, 2013.

G.-C. Yang and W. C. Kwong, Prime Codes with Applications to CDMA Optical and Wireless Networks. Norwood, MA, USA: Artech House, 2002.

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