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Int. J. Electron.Commun. (AE) 67 (2013) 868874

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InternationalJournal ofElectronics andCommunications (AE)

j ournal homepage : www.elsevier .com/ locate /aeue

Construction and generation ofOCDMA code families using a complete row-wiseorthogonal pairs algorithm

M. Ravi Kumar a,, P. Gangulyb, S.S. Pathak c, N.B. Chakrabarti c

a IIIT Bhubaneswar, Odisha, IndiabAdvanced Technology Development Centre, IIT Kharagpur, West Bengal, Indiac Dept. of Electronics & Electrical Comm. Engg., IIT Kharagpur, West Bengal, India

a r t i c l e i n f o

Article history:Received 19 November 2012Accepted 21 April 2013

Keywords:OCDMASpacewavelengthtime codesCode generationTi:LiNbO3

a b s t r a c t

A new code construction algorithm for incoherent Multi-Dimensional Optical Code Division Mul-tiple Access (MD-OCDMA) for asynchronous fiber optic communication is proposed. We refermulti-dimensionality to two-dimensional (2D) wavelengthtime or spacetime domains and three-dimensional (3D) spacewavelengthtime domains. The application of the algorithm in constructing2D multiple pulses per row codes and 3D multiple pulses per plane codes is given. The performance ofthecodes is discussed.In the applications discussed, this construction ensures a maximumcrosscorrela-tion of1 between any two codes. The proposed codes have complete 1D code allocation, which increasesthe cardinality. The performance ofsome codes in literature is compared with the proposed codes. Theanalyzedperformancemeasure is bit error rate due tomultiple access interference for different numbersofactive users. The performance analysis shows that the proposed 2D construction offers very low biterror rate at lower spectral efficiencywhen comparedwith other 2D constructions. A comparison oftheproposed 3D construction with existing 3D constructions shows lower bit error rate for equivalent codedimension. New integrated optic designs for the generation ofOCDMA codes using titanium indiffusedlithiumniobate technologyare explored,which can enable compact encoders anddecoders for computercommunications.

2013 Elsevier GmbH. All rights reserved.

1. Introduction

Optical Code DivisionMultipleAccess (OCDMA) is a futuremul-tiple access technology along with wavelength division multipleaccess and optical time divisionmultiple access [1]. The concept ofOCDMAis spreadingof a singlebit intomultiplebits.Suchblocksofmultiple bits are assigned distinctly to each user. These blocks aretermed as codes. Codes for incoherent OCDMA have to be unipo-lar orthogonal and constant weight to obtain low values of biterror rate due tomultiple access interference (MAI). A user trans-mits an assigned codewhenever a 1 is to be transmitted and does

not transmit anything whenever a 0 is to be transmitted [2]. Themajor advantage of OCDMA is its asynchronous behavior, whichconsiderably reduces optical resources required for timing syn-chronization. An OCDMA network may be one-dimensional (1D),two-dimensional (2D) or three-dimensional (3D), yielding Multi-Dimensional OCDMA (MD-OCDMA) [3].

Encoding a single pulse into a stream of pulses in the timedomain is termed as 1D spreading in the time domain [4,5]. The1D time-spreading OCDMA code families are represented as (T, K,

Corresponding author. Tel.: +91 8658872674.

a, c), where T is the temporal length of the code family, K isthe weight of the code family, a is the maximum out of phaseautocorrelationvalue of a code andcis themaximum crosscorre-lationvaluebetweenanytwocodes. The1Dopticalorthogonalcode(OOC) families have optimum values a =c=1 [5]. The construc-tion of 1D OOCs by the method of extended sets [5] is explainedin [6]. The optimum temporal length of 1D OOCs is given byTopt=K(K1)Nmax +1,whereNmax isthemaximumnumberofusersin thecode family, termed as cardinality.

Themajordrawbackof1DOOCsis therequirementof largetem-poral length. Using2D [7] or 3D [8] OCDMA, the cardinality of code

families canbe increasedby increasing the numberofwavelengthsor fibers and limiting thenumberof time chips. Thedisadvantagesof a code family with large temporal length are the necessity ofvery long fiber delay lines for encoding and decoding or very nar-row pulse widths (time chips). Instead of using lengthy fibers forencodinganddecoding,itisfeasibletousecompactintegratedopticdevices for these applications.

When a pulse is encoded into a 2D pattern of pulses in thewavelengthtime domain, the code families are represented as(W T, K, a, c), whereWis the number ofwavelengths and K istheweightof the 2DOCDMA code family.Whena pulse is encodedinto a 3Dpattern of pulses in thespacewavelengthtime domain,

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thecodefamiliesarerepresentedas(SW T,K ,a,c),where S isthenumberofspacechannelsorfibersandK istheweightofthe3DOCDMA code family. A 2DOCDMA code familymay be singlepulseper row (SPR) [7] or multipulse per row (MPR) [3,9]. Similarly, 3DOCDMAcode familiesmaybe single pulse per plane (SPP) [8,10] ormultipulse perplane (MPP) [3]. The advantageofmultipulse codesover singlepulse codes is the possibility of largerweight codes andlower bit error rate due to MAI, but at lower spectral efficiencyandhigher autocorrelation. For single pulsecodes[11,8],

a=0and

c1.In thispaper, constructionandperformanceofmultipulsecodes

usinga newalgorithmnamed complete row-wiseorthogonal pairs(CRWOP) for wavelength and/or fiber allocation is proposed andcomparedwithpreviouslyreportedcodefamilies[7,8,3]. Theinves-tigated performance measure of the code families is based oncardinality, code dimension (Cd) and the bit error rate due toMAI.Thebit errorrateequationfor hard-limitingreceiver,assumingchipsynchronous casefrom[4] fora threshold equal totheweightof thecode is used to derive the bit error rate due to MAI in 2D and 3Dcode families.

Based on some of the OCDMA code families discussed aboveand those proposed in this paper, designs for the generation of1D, proposed 2DMPRand 3DMPP code families using integrated-

optics are considered. Generation of these codes in thepicosecondregime using optical fiber delay lines is difficult due to the sub-micron precision of fiber lengths required. Optical delay in therange of picoseconds and sub-picoseconds is easier to generateby integrated-optics. The integrated optic devices discussed herearebased on titanium indiffused lithium niobate (Ti:LiNbO3) tech-nology. In order to design compact devices, the use of zero-gapdirectional coupler (ZDC) [12] is explored. The ZDCs are designedas TETM mode splitters to exploit the birefringence property ofLiNbO3.

The organization of this paper is as follows. Section 2 explainsthe proposed CRWOP algorithm to be used for wavelength and/orspatialallocation.Section3discussesthewaysinwhichtheCRWOPalgorithm is applied to 2D and 3D OCDMA systems. Section 4

compares and discusses the results of the performance analysis.The generation of codes using Ti:LiNbO3technology is explored inSection5, followed by conclusion in Section 6.

2. Proposed algorithm

The CRWOP algorithm is shown in the form of a flowchart inFig. 1. The numberofwavelengths (W>2) tobe used in the systemis the first parameter to be chosen. The number of 1D OOCs to beused in time domain, n is a function ofW. TheWwavelengths arearranged ina mannersimilarto thefrequenciesin aDTMFsignalinggrid. The first row contains wavelengths (w1, w2, . . . , wn) and thefirst columnhas wavelengths (wn+1, . . . , wW), wheren=W/2 .

The developmentof the CRWOPalgorithm is explainedwiththehelp of an example giving each step of the algorithm. ChoosingW=7,thevalueofn is calculated tobe4.A2Dgrid ofwavelengths isformedhaving4columnsand3rows.Each1DOOC( C1,C2, . . .,Cn) isallocated to each boxof the emptywavelength grid correspondingto pairs of wavelengths. The time allocation is by a cyclic shift ofthe 1DOOCs in successive rows.

Based on the allocation of 1D OOCs to wavelength pairs, thenext step creates an array according to wavelength pairs. In thenext step, the array formed in the previous step is sorted based onthe ascending order of users 1DOOCs.

Clubbing the wavelength pairs corresponding to same 1D OOCresults in theformationofcompleterow-wiseorthogonalpairs.Thearray generated by the CRWOP algorithm is a pair based design of

dimension n (Wn) with a wavelength crosscorrelation of zero

Fig. 1. Flowchart depicting the proposed CRWOPalgorithm.

in each row. The completeness of the CRWOP algorithm refers tothecompleteallotmentof wavelengths in therow-wiseorthogonal

pairs ofallthe rows ascompared to theRWOPcode families [3]. Fortheexample ofW=7, the final generated array is shown inTable1.

3. MD-OCDMA code construction

The pairs generated from the CRWOP algorithm can be appliedto construct 2D wavelengthtime and spacetime code fam-ilies. The CRWOP algorithm is also applied to construct 3Dspacewavelengthtime code families.

3.1. Construction of CRWOP-based 2D code families

ThewavelengthallocationoftheCRWOP-based2Dcodefamiliesis done as explained in Section 2. These code families have maxi-mum crosscorrelation and out-of-phase autocorrelation values of1 and 2 respectively. In these constructions, the required numberof 1DOOCs is given byn=W/2 . So the optimum temporal lengthof these 2D code families is given by Topt=K(K1)n+1, where Kistheweightof the employed1DOOC family. Theweightof these 2Dcode families is given by K =2K. An example 2D code family con-structed using 9 wavelengths is shown in Table 2. The code family

Table 1

Example of CRWOP generatedarray forW=7.

(w1, w5) (w4, w6) (w3, w7) C1(w2, w5) (w1, w6) (w4, w7) C2(w3, w5) (w2, w6) (w1, w7) C3(w4, w5) (w3, w6) (w2, w7) C4

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Fig. 3. Comparison of (a) MWOOC (541, 5, 1, 1); Nmax= 50; Cd= 205, (b) RWOP(1019, 4 , 2, 1); Nmax= 39; Cd=190 and (c) CRWOP (1315, 4, 2 , 1); Nmax=42;Cd=195 2D code families.

OOCs are detected simultaneously for any user, an error in detec-

tion ispossibleonly ifoverlapsfromthe interferingusersonallfourchannels are bit synchronous (T), so the bit error rate due to MAIfor the proposed 3D code families is

P

e =Pe(Nsi,wi )Pe(Nsi,wj )Pe(Nsj,wi )Pe(Nsj,wj )

T3 . (2)

The comparison of bit error rate due to MAI between CRWOP-based, RWOP-based and SPP 3D code families based on highest biterror ratedue toMAI of 2108 is shown inFig. 4. At high numberof active users, the bit error rate is equivalent for all the 3D codefamilies with a spectral efficiencyof 0.11 for the CRWOP-based 3Dcodefamilies,0.102for theRWOP-based3Dcodefamiliesand0.019for the SPP 3D code families. At low number of active users, theprobability of the SPP 3D code families is lower than that of the

CRWOP-based and RWOP-based 3D code families.Basedoncodedimension, comparisonof the biterror rate duetoMAI of (a) SPP [8], (b) RWOP-based and (c) CRWOP-based 3D codefamilies is shown in Fig. 5. Analyzing the characteristics between(a) and (c), the bit error rate of (c) is lower by a factor of 106 at aspectralefficiencyof 0.1154forCRWOPcomparedto 0.1423forSPP.From the characteristics of (b) and (c), the bit error rate is almost

20 30 40 50 60 70 80 90 100 11010

14

1013

1012

1011

1010

109

108

107

Number of active users

Probabilityoferr

or

CRWOP: S=4, W=15, T=17, Nmax

=112

RWOP: S=W=8, T=15, Nmax

=98

SPP: S=53, W=6, T=17, Nmax

=102

Fig. 4. Bit error rate due to MAI of CRWOP-based, RWOP-based and SPP 3D code

families.

50 100 150 200 250101410

12

1010

108

106

104

102

Number of active users

Probabilityoferror

(a)SPP

(b)RWOP

(c)CRWOP

Fig. 5. Comparison of (a) SPP (75 53, 7,0, 1); Nmax= 264; Cd=1855, (b) RWOP(101019, 8, 4, 1); Nmax= 171; Cd= 1900 and (c) CRWOP (121213, 8, 4, 1);Nmax= 216; Cd=18723D code families.

same ata spectral efficiencyof 0.1154for CRWOPcompared to0.09for RWOP.

5. Generation of OCDMA codes

The basic building blocks of most integrated optic devices arecouplers and splitters. The applications of these basic blocks areexplored for the generation of OCDMA codes.

5.1. Zero-gap directional coupler

Conventional integrated optic directional couplers have a gapbetween the two waveguides in the coupling region. Zero-gapdirectional couplers reduce the gap between the waveguides tozero resulting in a coupling region which has twice the width oftheindividualwaveguides. Thecouplingregionof theZDCsupports

two modes: a symmetric and an asymmetric mode. Separation ofTE and TM modes from one another needs to be explored for itsapplication in pulse pattern generation.

The proposed design is based on Ti:LiNbO3 technology, andtherefore, involves computing of the ordinary and extra-ordinaryrefractive indices (RI) for a set of parameters [13]. Effective-Indexbased Matrix Method (EIMM) [14] has been used to compute thepropagation constants and hence the critical coupling lengths ofthe ZDC for TE and TM polarizations. Based on the critical cou-pling lengths derived from the above cited procedures, normalizedpower coupling equation is used to choose a coupling length asrequired by the desired application.

The RI profile is modeled here as the sum of the RI given bythe Sellmeier equations and the change in RI induced by indif-

fusedtitanium.TheSellmeierequationsgoverning theordinaryandextra-ordinary RI are given by

n2o = 4.9048

0.11768

0.04750 w2

0.027169w2, (3a)

n2e = 4.5820 0.099169

0.04432 w2

0.021950w2, (3b)

wherew is thewavelengthofoperationinmicrometers.ThechangeinordinaryRI (no) andthe change inextra-ordinaryRI (ne) [13]are given by

no,e(x, z, w) =Ao,e(w, Cs)[C(x, z)]o,e , (4)

where Ao,e and o,e are constants independent ofx- and z-

coordinates, Cs is the surface concentration of indiffused titanium

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Lc

l1

l2 l3l4

TM

TE

A

B

C

D

i/p w

w

w

w 2w

Fig. 6. Proposed integrated optic zero-gap directional coupler.

and C(x, z) is the concentration of indiffused titanium. The con-centration of indiffused titanium for coupled waveguides [13] isrepresented by *

C(x, z, t) = 0.25C0

erf(+z)

dz+erf(z)

dz

erf(w+g/2+x)

dx

+erf (x +g/2)

dx+erf(w+g/2x)

dx+erf(x g/2)

dx

,

(5)

where w is the width of the single-mode waveguide,gis the gapbetween thewaveguides, is thethicknessof the titaniumlayer tobe deposited, t is the diffusion time and C0 is the initial concen-tration of titanium in z-cut LiNbO3 at t= 0 for 0z . Anotherparameter used in the simulation is diffusion temperature (),which is considered to be 1050C in all our simulations.

In our model, g=0 is considered because of the fact that ZDCimplies themutual joining of thetwoTitaniumstrips.However, theresult forg=0 as a wavelength divisionmultiplexer/demultiplexeris included in [12]. The parameters used for simulating theZDC in [12] are w = 7m, 2w = 14m, =0.095m, t=6h, w =1.318m and =1050 C. The operating wavelength of 1.3m ischosen corresponding to the secondwindow in optical fiber com-munications. For a ZDC shown in Fig. 6, w, and tshouldbe variedand checked such that a single mode is excited at the requiredwavelengthof operation. Replacingw with2w, the couplingregionmust excite two modes. If the coupling region does not excite twomodes, w, and thave to be varied repeatedly until two modesare excited in the coupling region. Simulation of RI profiles forw = 6.3m, 2w = 12.6m, =0.095m, t=6handw = 1.3m iscarried out.

The obtained RI profiles along theX-direction are sectored into3000 layers which are approximated to staircase-type step-indexprofiles according to [14]. The propagation of TE and TM modesthrough the ZDC is governed by the excitation efficiency given by

=

E+

g2

E+1

2

=

s22s11 s21s

12

s11(s11s22 s

21s

12)

2

, (6)

where E+1 is the incident electric field on the first layer, E+

g2 is the

incident electric field on an intermediate layer g2 having highestRI, the s-parameters are elements of a transmissionmatrix corre-spondingto all3000 layersandthe s-parameters areelementsof a

transmissionmatrix from thefirst layer to theg2th layer [14]. Eachvalue of1yields corresponding values of and , where 1is theangle of incidence of the electric field on the first layer and is thepropagation constant of the electromagnetic wave through all thelayers. The relationship between and 1is given by

=2

wn1 sin 1, (7)

where w is the operating wavelength and n1 is the RI of the firstlayer. The propagation constant () versus excitation efficiency ofTE and TMmodes for the ZDC shows the propagation constants ofa symmetric mode (s) and an asymmetricmode (a). The criticalcoupling length (Lc) for 100% power transfer [15] is given by

Lc=

s

a

. (8)

Lc

i/p

A

B

C

D

w

w2w

TM

TE

w

w

Fig. 7. Miniature1D OCDMA code generator using ZDC.

From theobtained propagation constants and using Eq. (8), thecritical coupling lengths of TE (Lc(TE)) and TM (Lc(TM)) modes arefound tobe 589mand 286mrespectively. Power transferequa-tions [15] for a directional coupler are given by

PC= 1 sin2 cy,

PD = sin2 cy,

(9)

where PCis the normalized power at port C, PD is the normalizedpower at port D, c=/2Lcand y is the direction of propagation.The variations in crosstalkbetween TEandTMmodesat the outputports with respect to the coupling length of the ZDC are calculatedas follows:

crosstalk (TE) =power of TMmodeatD

power of TEmode atDcrosstalk (TM)=

power of TEmode atC

power of TMmodeatC

(10)

The propagation length forwhich crosstalkis minimum forbothTEand TMmodes is chosen as the coupling lengthof the ZDC. Cor-responding toawavelengthof1.3m, thebestachievablecrosstalkis found tobe29.2dB and31.2dB for TEand TMmodes respec-tivelyat a coupling length of577m.The total length of the splitterincluding the length of the input and output arms is less than15mm.

In the design, distance between thetwo input ports is chosentobe the same as the distance between the two output ports, whichis 125m. This ensures proper coupling of optical fibers with thedevice. A value ofchosen as 1 is observed to provide a trade-off

between bending loss and electro-magnetic coupling at the inputand output junctions of the double mode region. The total lengthof the ZDC is the sum of lengths l1, l2, Lc, l3and l4(shown in Fig. 6),which comes to 11739.3m.

5.2. Ti:LiNbO3based 1D OCDMA code generation

Temporal spread 1D OCDMA codes can be generated by usingthe proposed TETM splitter as well as a 3dB power splitting Y-junctionrespectively.Thedelaybetweenpulses for the twodesignsis analyzed by assuming a standard dimension of LiNbO3 crystalsto be 50mm50mm1mm. This dimension has normally beenused as a standard in various applications.

A miniaturized OCDMA code generator using a ZDC (MOCG:Z)

on a standard LiNbO3 crystal is shown in Fig. 7. The code gener-ator is designed by extending and combining the output arms ofthe TETM splitter (Fig. 6). The code generator splits a single inputpulse into two output pulses spread in the time domain. The twooutput pulses of the code generator have orthogonal polarizations(TE andTM).Theissues indesigningthe1DOCDMAcodegeneratorare discussed and the calculations involved to find the time delaybetween the two pulses for the 1D OCDMA code generator in anideal case are shownbelow.

The 1D OCDMA code generator shown in Fig. 7 has a length of50mmand awidth of10mm.The curvedwaveguide is designed tohave negligible bending loss by drawing three arcs with a bendingradius of approximately 15mm. Starting from theoutput junctionof the ZDC, the length of the curved and straight waveguides in

Fig. 7 are 46861.6142m and 42762.9455m respectively. Fig. 7

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[19]. The loss of curved bends is simulated for a constant radius ofR=15mm. The excess loss due to curved bends is given by [20]

B = 4.34(2)L (dB), (16)

where 2 is the full width at half maximum of a resonance peakin propagation constant versus excitation efficiency plot for thesingle mode curved waveguide and L is the length of the curvedwaveguide. For R=15mm, 2 is 0.91109 for TE mode and

2.58810

9

for TM mode. Hence, the excess loss due to curvedbending is found to be 0.00017dB for TEmode and 0.00049dB forTMmodewith L =43360.3725m.

The optical pulse attenuation for the 1D code generator basedon the TETM splitter has two parts. One corresponds to the pathlength including the curvedwaveguide and the other correspondstothealternatepath(straightwaveguideafterTETMsplitter)fromthe input to the output of the device. The lengthof the curvedpathis 5.4cm and the length of the straight path is 5.0cm. Hence, theattenuation for the two paths would be 1.62dB and 1.5dB respec-tively. Four angular bendsareencountered inboth thepaths,whichputs the bending loss at 2.8dB [19]. The overall insertion loss forthe device comes toamaximumof7.42dB by ignoringthe low lossdue to curvedwaveguide.

The optical pulse attenuation for the 1D code generator basedon the 3dBpower splitting Y-junctionalso has the same two parts.SincetheY-junctionisshorterbyabout4mm,thelengthsofthetwopaths would be 5.0 cm and 4.6cm respectively. Thus, the attenua-tion for the two paths would be 1.5dB and 1.38dB respectively. Inthiscase,onlytwoangularbendsareencounteredin both thepaths,whichputsthe bending loss at1.4dB [19]. Theoverall insertionlossfor the device comes to a maximum of 5.9dB by ignoring the lowloss due to curvedwaveguide.

Similar overall insertion losses for the 2D and 3D code gen-erators based on the TETM splitter and the 3dB power splittingY-junctionwere carried out. From such analysis, it is observed thatthe insertion loss of the ZDC based devices is more than that ofthe 3dB power splitting Y-junction and is higher by around1.5dB.However, the delay performance as given in Section 5.2 supports

the suitability of TETM splitter.

6. Conclusion

The proposed CRWOP-based code families give better perfor-mance than theRWOP-based code families [3] andalso better thanthosepublishedearlier.The code families aresuitable fornetworkswhich are to be deployed with low error probabilities. Due tothe completeness of the wavelength/space allocation algorithm,the cardinality and spectral efficiency of the CRWOP-based codefamilies are marginally higher than that of the RWOP-based codefamilies.Thecodedimensionof theCRWOP-based 2Dcode familiesis lower than that of the RWOP-based 2D code families leading tohigher spectral efficiency at equivalent cardinality. However, the

bit error rate due toMAI ismarginally higher. The bit error rate ofthe CRWOP-based andRWOP-based code families is equivalent tothat of MWOOCs and SPP codes for full cardinality. The bit errorrate however is higher than SPP codes for small number of activeuserswhileyieldingbetter spectral efficiency. A comparison basedon code dimension shows that the CRWOP-based 2D and 3D codefamilies have lower bit error rate at higher spectral efficiency ascompared to theRWOP-based code families.The CRWOP-based2Dand3Dcode familieshave lowerbiterrorrateat lowerspectral effi-ciencywhencomparedwithMWOOCsandSPPcodesforequivalentcode dimension.

Refractive index profiles and propagation constants leading tothe critical coupling lengths are determined for deriving infer-ences to work out the dimension of the TETM splitter. Resultsshow that the cardinality is lower for the 3dB power splittingY-junction based devices than the TETM splitter based devices.The optical power calculations show lower insertion loss for the3dB power splitting Y-junction based devices than the TETMsplitter based devices. Hence, the 3dB power splitting Y-junctionbased devices would be suitable for OCDMA networks wherethe priority is given to low loss and the TETM splitter baseddevices would be suitable for OCDMA networks requiring largercardinality. A practical advantage of using the 3dB power split-ting Y-junction based devices is the absence of polarization modedispersion/distortion.

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