Applications and Constructions of Optical Codes With Large Cardinality and Multiple Tree Structures

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.

[1]  Guu-chang Yang,et al.  Design of multilength optical orthogonal codes for optical CDMA multimedia networks , 2002, IEEE Trans. Commun..

[2]  Giovanni Di Crescenzo,et al.  An Overlay Photonic Layer Security Approach Scalable to 100 Gb/s , 2008, IEEE Communications Magazine.

[3]  Shu Lin,et al.  Error control coding : fundamentals and applications , 1983 .

[4]  Ron M. Roth,et al.  On cyclic MDS codes of length q over GF(q) , 1986, IEEE Trans. Inf. Theory.

[5]  Ryoh Fuji-Hara,et al.  Optical orthogonal codes: Their bounds and new optimal constructions , 2000, IEEE Trans. Inf. Theory.

[6]  Wing C. Kwong,et al.  Optical Coding Theory with Prime , 2013 .

[7]  Guu-chang Yang,et al.  Performance comparison of multiwavelength CDMA and WDMA+CDMA for fiber-optic networks , 1997, IEEE Trans. Commun..

[8]  Guu-chang Yang,et al.  Optical orthogonal codes with unequal auto- and cross-correlation constraints , 1995, IEEE Trans. Inf. Theory.

[9]  Cheng-Yuan Chang,et al.  Multilevel Prime Codes for Optical CDMA Systems , 2009, IEEE/OSA Journal of Optical Communications and Networking.

[10]  Irving S Reed.  kth order near-orthogonal codes , 1971 .

[11]  Paul R Prucnal,et al.  Theoretical Analysis and Experimental Investigation on the Confidentiality of 2-D Incoherent Optical CDMA System , 2010, Journal of Lightwave Technology.

[12]  I. Andonovic,et al.  Hybrid wavelength hopping/time spreading schemes for use in massive optical networks with increased security , 1996 .

[13]  Fan Chung Graham,et al.  Optical orthogonal codes: Design, analysis, and applications , 1989, IEEE Trans. Inf. Theory.

[14]  Guu-Chang Yang,et al.  Design and Analysis of 2-D Codes With the Maximum Cross-Correlation Value of Two for Optical CDMA , 2008, Journal of Lightwave Technology.

[15]  P. Vijay Kumar,et al.  Large Families of Asymptotically Optimal Two-Dimensional Optical Orthogonal Codes , 2012, IEEE Transactions on Information Theory.

[16]  I. Reed,et al.  kth-Order Near-Orthogonal Codes (Corresp.) , 1971, IEEE Trans. Inf. Theory.

[17]  P.R. Prucnal,et al.  Optical Encryption With OCDMA Code Swapping Using All-Optical xor Logic Gate , 2009, IEEE Photonics Technology Letters.

[18]  László Györfi,et al.  Constructions of binary constant-weight cyclic codes and cyclically permutable codes , 1992, IEEE Trans. Inf. Theory.

[19]  Wing C. Kwong,et al.  Prime Codes with Applications to CDMA Optical and Wireless Networks , 2002 .

[20]  Wing C. Kwong,et al.  Extended Reed-Solomon Codes for Optical CDMA , 2013, IEEE Transactions on Communications.

[21]  Wing C. Kwong,et al.  Performance comparison of asynchronous and synchronous code-division multiple-access techniques for fiber-optic local area networks , 1991, IEEE Trans. Commun..

[22]  Guu-chang Yang,et al.  Multiple-length multiple-wavelength optical orthogonal codes for optical CDMA systems supporting multirate multimedia services , 2004, IEEE Journal on Selected Areas in Communications.

[23]  Oscar Moreno,et al.  A Generalized Bose-Chowla Family of Optical Orthogonal Codes and Distinct Difference Sets , 2007, IEEE Transactions on Information Theory.

[24]  Guu-chang Yang,et al.  Multiple-wavelength optical orthogonal codes under prime-sequence permutations for optical CDMA , 2005, IEEE Transactions on Communications.

[25]  Valdemar Cardoso da Rocha,et al.  Maximum distance separable multilevel codes , 1984, IEEE Trans. Inf. Theory.

[26]  A. Takada,et al.  Security in Photonic Networks: Threats and Security Enhancement , 2011, Journal of Lightwave Technology.

[27]  Cheng-Yuan Chang,et al.  Construction of Optimal 2D Optical Codes Using (n,w,2,2) Optical Orthogonal Codes , 2011, IEEE Transactions on Communications.

[28]  Guu-chang Yang,et al.  Shifted carrier-hopping prime codes for multicode keying in wavelength-time O-CDMA , 2005, IEEE Transactions on Communications.

[29]  T.H. Shake,et al.  Security performance of optical CDMA Against eavesdropping , 2005, Journal of Lightwave Technology.

[30]  Cheng-Yuan Chang,et al.  Extended multilevel prime codes for optical CDMA , 2010, IEEE Transactions on Communications.

[31]  Dwijendra K. Ray-Chaudhuri,et al.  Binary mixture flow with free energy lattice Boltzmann methods , 2022, arXiv.org.

[32]  Cheng-Yuan Chang,et al.  Wavelength-time codes with maximum cross-correlation function of two for multicode-keying optical CDMA , 2006, Journal of Lightwave Technology.