Performance Improvement of Duty-Cycle Division Multiplexing System Utilizing Symbol Coding Customization

Transcription

1 Performace Improvemet of Duty-Cycle Divisio Multiplexig System Utilizig Symbol Codig Customizatio M. N. DERAMAN 1, A. MALEKMOAMMADI, G. GNANAGURUNATAN, M. K. ABDULLA 3, K. DIMYATI 4, K. A. NOORDIN 4 1 Departmet of Commuicatio Techology ad Networkig, Uiversity Putra Malaysia, Malaysia Departmet of Electrical ad Electroic Egieerig, The Uiversity of Nottigham, Malaysia Research ad Developmet Departmet, Sigificat Techologies, Sd, Bhd, Malaysia 1 Departmet of Electrical Egieerig, Faculty of Egieerig, Uiversity of Malaya, Malaysia moord@upm.edu.my, amimalek_m@ieee.org Abstract: -This paper looks at the ovel method employed to improve the performace of the Duty-Cycle Divisio Multiplexig (DCDM) system. The proposed method ivolves sigal processig ad customisatio of the sigal at the trasmitter side. This techique regulates the amplitude level of existig waveform ito differet levels i such a way that the appropriate eye-height is icreased. The regulatio is made possible based o the feedback received accordig to the coditio of the received sigal set previously. This ovel method eables a 7 db improvemet i compariso to the covetioal model. I additio to that, performace for all trasmitted chaels is maitaied i cotrary to previous research outcomes. Key-Words: - Optical commuicatio, Multiplexig, Sigal processig, Duty cycle Divisio Multiplexig 1 Itroductio There is a plethora of multiplexig techiques that have bee developed for the purpose of augmetig the trasmissio capacity or badwidth i fiber optic trasmissios. Covetioally, most of such techiques are based o time, frequecy ad/or wavelegth domais amely Time Divisio Multiplexig (TDM) [1, ], Frequecy Divisio Multiplexig (FDM) [3] ad Wavelegth Divisio Multiplexig (WDM) [, 4]. TDM for example, divides the time ito several recurret time slots of certai duratio to accommodate a fixed umber of sub-chaels. Each user is give a specific time slot i order to trasmit. Thus, the full trasmissio ability of high capacity trasmissio medium ca be utilized by multiplexig several users data i the time domai. owever, this capacity ca be further icreased by itroducig a ew multiplexig techique amely Duty-cycle Divisio Multiplexig (DCDM). The DCDM, first itroduced by [5] proposes the idea of utilisig differet RZ s dutycycle for each user. Differet user sigal waveforms are multiplexed i a chael withi the same time period ad at the same wavelegth (or frequecy). I this case, the sigals are ecoded from multiple users data with differet properties of duty-cycle ad power level (amplitude). Therefore, DCDM is a multiplexig techique, which serves the dual fuctio of data ecodig ad combiig the subchaels durig trasmissio. Thece, the trasmissio of multiple users data over a sub-chael i a medium ca be materialized through capitalizig both the time ad wavelegth domais, which i tur icreases the total chael capacity. I [5], simultaeously trasmittig data over DCDM waveforms outperform other modulatio scheme amely TDM [5, 6]. owever, oe disadvatage of a early DCDM techique is that the performace of various chaels is ot uiform [7]. For istace, at a BER of 10-9, the receiver s sesitivity is recorded to be at -3 db, -6.5 db ad -30 db for User 1 (U1), User (U) ad User 3 (U3), respectively. The discrepacy is particularly obvious betwee U1 ad U3. This situatio will itroduce difficulties i a eviromet where a commo trasmissio stadard is required. For example, it is costly to characterize ad defie the trasmissio capability due to the requiremets of differet receiver s sesitivities. Furthermore, itelliget receivers are required to differetiate the icomig waveform/sigal from each chael. Thus, the focus of this paper is (a) to improve the performace of DCDM ad (b) to reduce the performace discrepacies betwee the multiplex chaels. This is achieved through customisatio of the amplitude levels of the DCDM symbols at the trasmitter side based o the feedback received accordig to the coditio of the received sigal set earlier. E-ISSN: Volume 14, 015

2 This approach is able to cushio the impairmets due to oise ad dispersio, which directly iflueces the BER. The outlie of this paper is as follow: at the outset, brief history about DCDM icludig the workig priciples ad a explaatio of the DCDM simulatio setup are ivolved. The power levels fuctio associated with the eye-opeig are also elaborated here. Followig this, the eyeopeig of the DCDM sigal i relatio to the performace of each user is discussed i the subsequet sectio. I order to substatiate the proposed method, the simulated results are reported ad discussed i the subsequet sectio. DCDM WORKING PRINCIPLE AND TE SIMULATION SETUP Fig. 1 shows the block diagram of the simulatio setup of the Duty-Cycle Divisio Multiplexig (DCDM) system. It comprises three mai compoets amely trasmitter, commuicatio medium ad the receiver. The trasmitters are geeratig data at PRBS of 3-1 at 10 Gb/s ( per chael). The icomig user s data are fed ad coverted from o-retur to zero (NRZ) to retur to zero (RZ). 1 (t/cr) e 0 t < t1 1 t1 t < t E(t) = (t/cf ) e t t < tc 0 tc t < ts (1) where cr ad cf are the rise time ad fall time coefficiet, respectively. The t1 ad t, together with cr ad cf are umerically determied so that pulses with the exact values of the rise time ad fall time will be geerated. tc is the duty cycle value, which represets the duratio of high level withi a bit period, ad ts is the bit period. All users data are multiplexed usig a power combier (electrical adder) resultig i a DCDM sigal. The DCDM symbol mimickig stair case is established. For istace, if U1, U ad U3, are carryig bit 0 s, the DCDM waveform patter ca be see i Case 1 i Fig.. Meawhile, bit period (Ts) of each waveform is associated with four slots (Slot1 Slot4). The umber of slots is associated with the umber of icomig users followig (+1) rule, where is the umber of users. These slots are due to the RZ duty-cycles of origial users symbol duratio. Meawhile the combiatio of the origial user s sigal amplitude level cotributes to the amplitude of the waveform. As show i Fig. (d) the geerated DCDM sigal has specific patters. These symbol patters are characterized by differet duty-cycle ad power level associated with each user. Fig. 1: The simulatio setup for DCDM system (10 Gbit/s per chael) The pulse shape used i the aalysis is Gaussia, represetig the RZ format, which ca be described by [8]. Fig. : (a) Possible DCDM patter for U1. (b) Possible patter for U. (c) Possible patter for U3. (d) Multiplexed sigal for U1, U ad U3. The DCDM data is modulated through costat wave (CW) laser diode at 1550 m wavelegth. Usig a exteral modulator; the optical field at the output of the optical modulator is give by [9]. E-ISSN: Volume 14, 015

3 E out ( t) = E ( t).cos( θ ( t)).exp( j. ϕ( t)) i () where E i (t) is the optical field at the iput of the MZM, Θ is the phase differece betwee the two waveguide braches i MZM ad Φ is the sigal phase chage defied as : ϕ = SC θ ( t) (1+ SF) /(1 SF) (3) I Equatio (3), the parameter SC is ±1 if egative sigal chirp is disabled or eabled, respectively, ad SF is the symmetry factor. The fiber is modelled usig a low pass equivalet represetatio of a liear badpass system i which the fiber dispersio is accouted through the quadratic (oliear) phase respose of the fibers trasfer fuctio, give by [8] fib ΠDLλ ( f ) = exp j ( α. L / ) c f (4) where, λ is the operatig wave legth (1550 m), c is the free-space speed of light, D=17 ps/(km.m) is the fiber s liear dispersio coefficiet, L is the fiber legth, ad α is the atteuatio coefficiet. Next we assume a EDFA gai, equal to G at the operatig wavelegth ad amplified spotaeous emissio (ASE), sp The optical power P (t) is give by [8]. P( t) = G s( t)[ ( t) cos ( t) ( t)si ( t)] G ( t) [ ( t) t 1 c ϕ + s ϕ c c c S c c s ( )] s (5) where the coefficiets c1 ad c are the iput ad output couplig losses of the optical pre-amplifier, respectively ad s(t) is the received amplitude of the optical field at the receiver. The oise process is described by two zero mea Gaussia distributed radom variables, c (t) ad s (t), correspodig to the i-phase ad out-of-phase oise compoets of the bad limited oise process, respectively. The power spectral desity of the ASE oise, per polarizatio, is give by [8-9] N ASE = ( G 1) hv sp (6) where hv is the photo eergy. The variace (power) of the radom variables is therefore σ = P ASE = ( 1) B G hv sp 0 S c (7) where B 0 is the oise equivalet badwidth of the optical filter. At the receiver side, the optical sigal is detected by a photodiode ad passed through a low-pass filter (LPF) ad Clock-ad-Data-Recovery (CDR) uit. The photodetectio is icorporated i to the model as a Poisso process with itesity η λ( t) = P( t) + λ0 hv (8) where η is the quatum efficiecy of the power λ 0 coversio process ad is the dark curret. From (8), the mea (9) ad variace (10) of the detectio curret are derived c c s h E[ I ] = R G ( t)* ( t) + (0) (0) d s 1 e PASE Rs + q e 0 e σ = q I d ~ r( f ). R c c s 1 s ( t) * he ( t) + q o( f ) * * e( f ) j ft. R c s (9) (10) where R s is the resposivity of the photodiode which qη is equal to hv, where q is the electro charge, h e (t) ad e (0) are the impulse respose ad the DC gai of the electrical filter, respectively. I (11), B e is a measure of the oise equivalet badwidth of the electrical filter. Be ( f ) e df (11) The oise badwidth of the ASE-ASE beat oise is measured through I, which is calculated by [11] I = (1) where e (f) ad o (f) are trasfer fuctios of the electrical ad optical filter, respectively. The cotributio from the thermal oise was also added as a additioal term i (10). After the sigal passes through the trasmissio medium ad reaches the receiver ed, the sigal detectio ad bit regeeratio takes place. I order to decide o the icomig sigal, the iferece rules are used as show i Table I. The decisio is based o the fixed threshold values, which is assiged ito P c o( f ) ASE B e + 4 df + = e( f ) o( f ) * o( f ) s G 1 R c c q λ B 0 df N e + λ ASE s R c N ASE I E-ISSN: Volume 14, 015

4 three differet values associated with each level (th1, th ad th3). To describe this, cosider Case 1 i Fig. (d). I this example, the received sigal amplitude is less tha th1, which refers to the first rule i Table I, the receiver (R1) is assumed to receive a bit 0. Table I: The Decisio Makig Rules No User Rule 1 U1 if (S1 < th1)&(s < th1) U1 if (th3 S1 < th)&(th15 S < th4) 3 U1 if (th S1 < th1)&(s th4) 4 U1 if (th3 S1 < th)&(s < th5) 5 U1 if (th S1 < th1)&(th5 S < th4) 6 U1 if (S1 th1)&(s th4) 7 U if (S < th5)&(s3 < th6) 8 U if (th5 S < th4)&(s3 th6) 9 U if (th5 S < th4)&(s3 < th6) 10 U if (S th4)&(s3 th6) Decisio Case 1 U5=0 3, 5 U5=0 U5=0 U5=1 U5=1 U5=1 U50=0 U50=0 50=1 U50=1 11 U3 if (S3 < th6) U75=0 1 U3 if (S3 th6) U75=1 7 4, 6 8 1, 5, 6 3, 4 7, 8 1,, 3, 4 5, 6, 7, 8 Note that the DCDM simulatio setup icludes a Arbitrary Waveform Geerator (AWG) [11] before the Match-Zehder Modulator (MZM). The fuctio of the AWG i this case is to modify the trasmitted power level accordig to the eye-opeig requiremets (the workig priciple of AWG will be elaborated i depth heceforth). The implemetatio of AWGN makes it differet from [10] thereby eablig power level regulatio. The power level of trasmitted waveform ca be regulated at several stages or levels accordig to BER requiremets at the receiver. These modified sigals are trasmitted through 80 km sigle mode fiber (SMF). The dispersio effect is egligible due to the use of dispersio compesatio fiber (DCF). The mai fuctio of AWG is to set the trasmitted amplitude for each level. I doig so, a mappig fuctio is used (see Table II). It ca be implemeted as a simple algorithm embedded i the AWG. Its fuctio is to combie the source bit sequece (three bits) of the idividual users ad trasform them ito a DCDM sigal. This sigal or symbol ca be customised as required so as to icrease the vertical eye opeig. For example, cosider that a 111 user s bits combiatio, the origial amplitude levels (3,, 1) will produce a eye-patter as show i Fig. 3. I order to icrease the eye-1 of Fig. 3(a), the amplitude level eeds to be decreased (i this case, the amplitude level 3 caot be icreased sice the maximum power level is 1). With that approach, oe ca icrease the height of eye-opeig of eye-1 as i Fig. 3(b). I the perspective of DCDM level, the origial level of Level, which is takig the value of, ca be attued to 1.8. Idirectly, this will icrease the eye- 1 high. owever, the effect of this techique is set to reduce the eyes relates to the eighbourig levels (eye- ad eye-3). This effect caot be avoided due to the limited sigal space with regard to the power set. As the symbol reaches the receiver, the direct detectio method is used to covert the DCDM sigal ito the electrical sigal. The sigal is recovered based o the settig threshold level by a decoder circuit as implemeted i o-off keyig systems [9]. I order to decide o a sigle bit, the rules based o decisio-makig are cosidered [8,10] as multiple slots ad levels are ivolved. For istace, S1 ad S are used to decide o the bit sequece for U1 whereas S ad S3 are used for U ad Slot 3 (S3) for U3. This simulatio setup is slightly differet from that of [7] i terms of level spacig mechaism ad the AWG implemetatio. I [5], a specific coefficiet fuctio is used to regulate the power level 1 ad power level with the same coefficiet rate (see Fig. 3). Apart from that, the approach used i this research allows separate spacig values betwee two levels without the eed to follow a specific coefficiet value. Thus, the eyes i each associated levels ca be further attued to achieve a better BER with customised spacig criteria. The spacig value ca be set by ruig customisatio algorithm, o the AWG through a feedback chael [11-13] ad by settig the associate amplitude at various levels. This implemetatio, mimickig [14], is where a E-ISSN: Volume 14, 015

5 adaptive trasmitter is used to chage its modulatio format to/from BPSK, QPSK ad QAM. The feedback chael i this case utilizes geeralpurpose iterface bus (GPIB) to sed the amplitude ad phase requiremet to the trasmitter. The same out-of bad chael feedback is used i [1]. A state geerator is located just before the receiver ad is used to moitor the active chael ad sed the feedback state to the trasmitter. Table II: Bit-to-sigal Mappig Fuctio Bits combiatio from U1, U ad U3 Origial level per slot (Slot 1, Slot ad Slot 3) New amplitude level (Slot 1, Slot ad Slot 3) 000 0, 0, 0 0, 0, , 0, 1 0, 0, , 1, 0 1, 1, 0 011,, 1, 1.8, , 0, 0 1, 0, 0 101, 1, 1, 1, 1 110,, 0, 1.8, ,, 1 3, 1.8, 1 limited ad time-cosumig as the log spa system is curretly beig ivestigated [15]. Istead, the probability method based o Q value is used i this study to evaluate the performace [5, 6]. The assumptio of Gaussia oise o bits 0 s ad 1 s i relatio with its mea value ad the stadard deviatio for each level are used i this study. The quatity, Q is give by: (13) where µ ad σ are the meas ad the stadard deviatios for each of the eyes, respectively. The BER ca be calculated based o (13) ad is give by (14) The basis of BER calculatio i DCDM is based o Fig. 3, ad it is associated with the respective received eyes i Fig. 4. The probability of errors (Pe) of each eye ca be associated with Pe s of the respective eye. For istace, at eye-6 (Fig. 3), the Pe is associated with PeI ad Pe of Fig. 4. Thus, the Pe at eye-6 is best described by Pe(eye-6) = ½ *(Pe+PeI); (15) where Pe is the probability of error beig 0 ad PeI is the probability of errors of beig 1. Both are error probabilities at eye-6 based o its threshold value of th6. As stated i Table I, the data recovery ad BER calculatio for U3 is oly related with rules 11 ad 1 where it ca be described as if (S3 <th6) U3 = 1 else if (S3 th6) U3 = 1 (16) thus, the error probability for U3 is described as BERU3 = Pe(eye-6) (17) Based o the combiatio of these simple rules ad the associated Pe of each eye, the BER for idividual users ca be summarized as follows: Fig. 3: (a) origial eye-opeig. (b) eye-high for eye-1 is icreased 3 BER CALCULATION Bit error rate (BER) is basically the ratio betwee eroded received bits over total received bits. This is the best method to calculate the BER, but it is BER U1 = ½ *((PeA + PeBm*PeFs + PeCm*PeG) + (PeBs*PeE + PeCs*PeFm + PeD)) (18) BER U = ½ *((PeE + PeFm*PeI) + (PeFs*Pe + PeG)); (19) E-ISSN: Volume 14, 015

6 BER U3 = ½ *(Pe+PeI); (0) For BER of U1, several Pe ivolves; PeA is the error probability associated with eye-1. Sigal C D A B th3 th S1 S S3 Probability Fig. 4: probability of errors E F G The PeA comes ito picture whe the amplitude level is beyod level-3. The ext Pe s parameters are PeBm ad PeFs. These two parameters are associated with level- but i betwee two adjacet slots (S1 ad S). It is logic to assume that (see Table I) to determie the bit sequece, two slots will be examied. I this case, the error is to be compesated by each other s slot. Thus, i the mathematical formula, multiplyig the Pe of S at the same level ca reduce the Pe i S1. The error ca be reduced if the both Pe values are less tha 1. Sice, PeA ad PeD do ot have its pair to compesate; it is sigificat to decrease this value. PeA was chose owig to the ease i elargig the eye-1 with less effect to the other slots as compared with PeD. The calculatio of Pes is based o the received eye patters. This is solely depedets o the size of the eye. The larger the vertical eye-opeig the more oise tolerated at the receiver side [15, 16]. I this case, each Pe is associated with differet user s BER. Thus, it is importat to choose which Pe ad eyes are ivolved with the target user s BER. I th1 By regulatig the power level at trasmitter, it is believed that impairmets such as oise will be cushioed. From this poit of view icreasig the trasmitted power level leads to eye-high icremets at the receiver side, which cosequetly ca reduce the BER. Not that the higher the level of sigal amplitude the lower the probability of the error. As a example, at eye-6 (i Fig. 3), by icreasig the amplitude of the level 1, the value of Pe ad PeI will reduce accordigly, which leads to better performace for U3. Note that the mai aim is to optimize the level distributio betwee differet eyes while the maximum amplitude is fixed. 4 Results ad Discussio I the first stage, the simulatios were coducted to optimize the eye-opeig of specific eye while the maximum voltage level is fixed. Eye-1 was chose sice its probability of error (Pe) was high. Furthermore, Pe for eye-1 solely cotributed to BER calculatio of U1, as it could ot be compesated by aother Pe from other slots. Nevertheless, PeD was quite low due to the larger eye-opeig of eye-4 as discussed above ad show i Fig. 3(a). Fig. 5 shows a improvemet of more tha 1dB at the BER of 10-9 as compared to the previous result reported i [6] for the U1. This was achieved by icreasig the high-opeig of eye-1 to 10%. Further improvemet of db could be obtaied whe the eye height reached 130%. It was actually due to the sigificat reductio of the probability of error of eye-1, PeA. As the opeig of Eye-1 icreased towards 140%, it gave a egative impact to the BER. This was due to the limitatio of a amplitude level i DCDM waveform where all users had to share the same sigal space. Note that as show i Fig.3 (b) i order to maitai the maximum amplitude level, icreasig the eye high i eye 1 automatically results i reducig the eye high for eye, which, i tur will affect the performace of U. Therefore based o the simulatio results, show i Fig. 6, i order to maitai the acceptable performace for U, the eye high for eye1 ca be icreased by maximum of 10%. As show i Fig. 7, chael 3 (U3) still outperforms as compared to U ad U1. By this optimizatio, the performace of chael 1 ad are closed to each other but still there is a huge gap betwee the performace of these two chaels ad chael 3. E-ISSN: Volume 14, 015

7 Fig. 5: The effect of varyig level o the receiver sesitivity of chael 1 optimizatio affects the sesitivity of U3 as it degrades by db, but it is still withi the acceptable BER of As show i Fig. 8 ad as opposed to the previously reported work [5], these optimizatios, leads to almost same performace for all three chaels. With this so-called optimum power settig level, the calculatio is exteded usig differet fiber legth ad dispersio levels. For the first sceario, the SMF fiber legth is varied ragig from km. The amplifier is set before the receiver with oise figure (NF) of 5 db ad a gai of 30 db. The plotted results for the SNR over fiber legth ca be see i Fig. 9. As expected, the SNR for the amplified sigal is higher as compared to the oamplified oe. It is particularly obvious whe the fiber is less tha 70 km. owever, as for both cases, the customised trasmitted power level leads to db improvemets i terms of SNR. Fig. 6: The effect of icreasig eye-height of eye-1 to the performace of U Fig. 8: performace compariso betwee the covetioal chaels (BER of U1, ad 3) ad the optimized chaels (ew BER for U1, ad 3 Fig. 7: Performace compariso betwee all three chaels after the optimizatio I order to decrease the gap betwee the performaces of all three chaels, the amplitude of level is adjusted to 1.4 whilst Level 1 is set to 0.4 (istead of 1). Thus, the gap betwee Level 3 ad Level is icreased to 160% whilst the gap betwee Level ad Level 1 is slightly decreased to 98%. As a result of this adjustmet, the gap betwee Level 1 ad Level 0 is reduced to oly 4%. It shows that the receiver sesitivity at this poit icreased to 7 dbm (at the BER of 10-9 ). Note that this Meawhile, i the perspective of the fiber spa, the o-customised level is out performed for the fiber legth less tha 84 km. I the ormal circumstaces, the BER performaces will follow the SNR. I this case, the customised level will improve the performace by reducig the BER. owever, it is ot exactly the case i DCDM as its decisio, depedets o more tha oe slot. Furthermore, the SNR actually decreases whe the trasmitted power level is mitigated. owever, with referece to Fig. 5, the simulatio results show that with a extesio offered i the decisio rules, the performace of the system improved greatly. This proves that by referrig to other slots, the decisio-makig is more accurate owig to the egatio of oise effects. Meawhile, as show i Fig. 10, by icreasig the dispersio from 80 ps/m/km to 98 ps/m/km the BER of U1 chages i a liear fashio from 10-4 to E-ISSN: Volume 14, 015

8 owever, this is irrelevat with the U ad U3 as the proposed techique will icrease the BER for both users. This shows that the U1 is depedet o the impairmet from dispersio sice its decisiomakig ivolves S1 ad S oly. Fig. 9: SNR over fiber legth Fig. 10: log BER versus dispersio 5 Coclusio We have proposed ad developed a ovel method to improve the performace of the DCDM system. Utilizig the sigal processig methods ad customisatio of the sigal level at the trasmitter side, 7 db improvemets i compariso to the covetioal DCDM system was achieved. I additio to that, ad as opposed to the previously reported work, all chaels show almost the same performace Refereces: [1] E.S assa, Performace Ehacemet of Cotiuous-Phase Modulatio Based OFDM Systems Usig Chaotic Iterleavig WSEAS trasactios o systems. vol. 1, 013 [] A. Rudziński. Effective Number of Samples ad Pseudo-Radom Noliear Distortios i Digital OFDM Coded Sigal. Circuits, Systems, ad Sigal Processig. Vol. 33, 014, pp [3] D. Sheela, C. Chellamuthu, A Cost Effective Approach for WDM Network Protectio uder Critical Duct Costraits, WSEAS Trasactios o Commuicatios, vol.11, 01 [4] G. A. Mahdiraji, A.F. Abas, A. Malekmohammadi, M. Mokhtar, Duty-Cycle Divisio Multiplexig: Alterative for igh Speed Optical Networks. Japaese Joural of Applied Physics. Vol. 48, 009 [5] G. A. Mahdiraji, et al., Duty-Cycle-Divisio- Multiplexig: Bit Error Rate Estimatio ad Performace Evaluatio, Optical Review, vol. 16, 009, pp [6] A. Malekmohammadi, G.A. Mahdiraji, M.K. Abdullah, A.F. Abas, M. Mokhtar, M. F. A. Rashid, Absolute Polar Duty Cycle Divisio Multiplexig, Iteratioal Review of Electrical Egieerig, vol. 3, 008, pp [7] A. Malekmohammadi, M.K. Abdullah, G.A. Mahdiraji, A.F. Abas, M. Mokhtar, Aalysis of retur-to-zero-o-off-keyig over absolute polar duty cycle divisio multiplexig i dispersive trasmissio medium, IET optoelectroics. Vol. 3, 009, pp [8] A. Malekmohammadi, G.A. Mahdiraji, A. Abas, M.K. Abdullah, M. Mokhtar., Effect of selfphase-modulatio o dispersio compesated absolute polar duty cycle divisio multiplexig trasmissio, IET Optoelectroics, vol. 3, 009, pp [9] S.T. Cudiff ad A. M. Weier, Optical arbitrary waveform geeratio Nat Photo. Vol. 4, 010, pp [10] U. Erez ad R. Zamir, Noise predictio for chael codig with side iformatio at the trasmitter, IEEE Trasactios o Iformatio Theory, vol. 46, 000 [11]. Y. Choi, T. Tsuritai, ad I. Morita, BER-adaptive flexible-format trasmitter for elastic optical etworks. Optics Express, vol. 0, 01, pp [1] T. Liu, et all, Feedback chael capacity ispired optimum sigal costellatio desig for high-speed optical trasmissio, i Cof. Lasers ad Electro-Optics, USA, 01 [13] C.J. Aderso ad J.A. Lyle Techique for evaluatig system performace usig Q i umerical simulatios exhibitig iter symbol iterferece, Electroics Letters. Vol. 30, 1994, pp E-ISSN: Volume 14, 015

9 [14] G. Kaddoum, J. Athoy, P. Lawrace, C. Roviras, Chaos Commuicatio Performace, Theory ad Computatio. Circuits, Systems, ad Sigal Processig, vol. 30, 011, pp [15] A. Malekmohammadi, M.K Abdullah, G. A Mahdiraji, A.F. Abas, M. Mokhtar, M. F. A Rasid, S.M. Basir, Decisio circuit ad bit error rate estimatio for absolute polar duty cycle divisio multiplexig Iteratioal Review of Electrical Egieerig, vol. 3, 008, pp [16] M.N. Derahma, M.K. Abdullah, N.K. Dimyati, ad A. Malekmohammadi, Symbol codig customizatio for BER reductio i Duty-cycle Divisio Multiplexig Systems i Cof. 18th Iteratioal Coferece o Commuicatios (part of CSCC '14), July 17-1, 014 E-ISSN: Volume 14, 015