Beyond 100 Gb∕s Optical Transmission Based on Polarization Multiplexed Coded-OFDM With Coherent Detection

50 J. OPT. COMMUN. NETW./VOL. 1, NO. 1 /JUNE 2009 Djordjevic et al.

Beyond 100 Gb/s Optical TransmissionBased on Polarization Multiplexed

Coded-OFDM With Coherent DetectionIvan B. Djordjevic, Lei Xu, and Ting Wang

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Abstract—We propose a coded-modulation schemesuitable for beyond 100 Gb/s transmission and100 Gb/s Ethernet. It is based on polarization multi-plexed coded-orthogonal frequency division multi-plexing (OFDM). By using 32-QAM-based polarizationmultiplexed coded-OFDM, we are able to achieve theaggregate rate of 100 Gb/s, while the OFDM signalbandwidth is only 10 GHz, resulting in a spectral effi-ciency of 10 bits/s /Hz. The spectral efficiency of theproposed scheme is twice higher than that of the po-larization diversity OFDM scheme. We show that theproposed multicarrier scheme is insensitive to polar-ization mode dispersion (PMD), while the PMD repre-sents a major source of performance degradation insingle carrier systems, in addition to fiber nonlineari-ties. We also describe how to determine the symbols’log-likelihood ratios in the presence of laser phasenoise.

Index Terms—Optical communications; Polariza-tion mode dispersion (PMD); Low-density parity-check (LDPC) codes; Polarization diversity; Polariza-tion multiplexing; Orthogonal frequency divisionmultiplexing (OFDM); 100 GbÕs Ethernet.

I. INTRODUCTION

O ptical communication systems are developingrapidly due to the increased demands on trans-

mission capacity. Network operators already consider100 Gb/s per dense wavelength division multiplexing(DWDM) channel transmission. However, the perfor-mance of fiber-optic communication systems operatingat those data rates is degraded significantly due toseveral transmission impairments including intra-and inter-channel nonlinearities, polarization modedispersion (PMD), and chromatic dispersion [1–14]. To

Manuscript received October 19, 2008; accepted December 29,2008; published June 1, 2009 �Doc. ID 110471�.

I. B. Djordjevic is with the University of Arizona, Department ofElectrical and Computer Engineering, Tucson, AZ 85721, USA(e-mail: [email protected]).

L. Xu and T. Wang are with NEC Laboratories America, Princeton,NJ 08540, USA.

Digital Object Identifier 10.1364/JOCN.1.000050

1943-0620/09/010050-7/$15.00 ©

eal with chromatic dispersion and PMD a number ofhannel equalization techniques have been proposedecently, including a digital filtering approach [11,12],aximum likelihood sequence detection (MLSD) [4,9],

nd turbo equalization [2,8]. To simultaneously sup-ress chromatic dispersion and PMD, orthogonal fre-uency division multiplexing (OFDM) has been advo-ated [5–7,10]. To deal with intra-channelonlinearities someone may use either constrainedoding [3] or turbo equalization [8].

In this paper we propose a coded-modulationcheme suitable for beyond 100 Gb/s optical transmis-ion based on coded-OFDM and polarization multi-lexing. By using 32-QAM polarization multiplexedoded-OFDM we are able to achieve the aggregateata rate of 100 Gb/s for OFDM signal bandwidth ofnly 10 GHz, resulting in a spectral efficiency of0 bits/s /Hz. The tolerance to PMD of the proposedcheme is comparable to the corresponding polariza-ion diversity scheme, but offers two times higherpectral efficiency. (Notice that we use the term diver-ity in the same fashion that is used in wireless com-unications [15,16], which is different from the polar-

zation multiplexing [11], and denotes that the sameymbol is transmitted using both polarizations.) Whilehe PMD in single carrier systems at high speeds rep-esents a major performance degradation factor (inddition to Kerr nonlinearities), the penalty due toMD in the proposed coded-modulation scheme isegligible.The arbitrary forward error correction (FEC)

cheme can be used with the proposed polarizationultiplexed coded-OFDM scheme. However, the use of

arge-girth low-density parity-check (LDPC) codes14] leads to the channel capacity achieving perfor-ance. We also describe how to determine the sym-

ols’ reliabilities (i.e., the symbol log-likelihood ratios)n the presence of laser phase noise.

II. DESCRIPTION OF THE PROPOSED POLARIZATIONMULTIPLEXED CODED-OFDM SCHEME

It has been shown by Shieh et al. in [5–7] that theolarization diversity OFDM is able to compensate

2009 Optical Society of America

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Djordjevic et al. VOL. 1, NO. 1 /JUNE 2009/J. OPT. COMMUN. NETW. 51

all-order PMD with small penalties. Moreover, thePMD improves the system margin for PDL-inducedpenalty [7]. Therefore, for evaluation of differentOFDM schemes it is sufficient to observe the first-order PMD. For the first-order PMD study the Jonesmatrix, neglecting the polarization-dependent lossand depolarization effects due to nonlinearity, can berepresented in a fashion similar to [13] by

H�� = �hxx�� hxy��

hyx�� hyy�� = R−1P��R,

P�� = �e−j��/2 0

0 ej��/2� , �1�

where � denotes DGD, R=R�� ,�� is the rotational ma-trix defined by

R = � cos��/2�ej�/2 sin��/2�e−j�/2

− sin��/2�ej�/2 cos��/2�e−j�/2� , �2�

� denotes the polar angle, � denotes the azimuthangle, and � is the angular frequency. For coherentdetection OFDM, the received symbol vector ri,k= �rx,i,kry,i,k�T at the ith OFDM symbol and kth subcar-rier can be represented by

ri,k = H�k�si,kej�PN + ni,k, �3�

where si,k= �sx,i,ksy,i,k�T denotes the transmitted sym-bol vector, ni,k= �nx,i,kny,i,k�T denotes the noise vectordue to the amplified spontaneous emission (ASE), andthe Jones matrix H was introduced in Eq. (1). Here weuse index k to denote the kth subcarrier frequency �k.�PN denotes the phase noise process �PN=�T−�LO dueto the laser phase noise processes of transmitting la-ser �T and local laser �LO that are commonly modeledas the Wiener–Lévy processes [17], which are zero-mean Gaussian processes with corresponding vari-ances being 2��T�t� and 2��LO�t�, where ��T and��LO are the laser linewidths of the transmitting andreceiving laser, respectively. The transmitted/receivedsymbols per subcarrier are complex-valued, with thereal part corresponding to the in-phase coordinate andthe imaginary part corresponding to the quadraturecoordinate of a corresponding signal constellationpoint. Figure 1 shows the magnitude responses of thehxx and hxy coefficients of the Jones matrix against thenormalized frequency f� (the frequency here is nor-malized with DGD � so that the conclusions are inde-pendent on the bit rate) for two different cases: (a) �=� /2 and �=0, and (b) �=� /3 and �=0. In the firstcase channel coefficient hxx tends to zero for certainfrequencies, while in the second case it never becomeszero, suggesting that the first case represents theworst case scenario, and as such is considered in Sec-tion III.

The proposed coded-OFDM scheme, with an LDPCode as the channel code, is shown in Fig. 2. The bittreams originating from m different informationources are encoded using different �n ,ki� LDPC codesf code rate ri=ki /n. ki denotes the number of infor-ation bits of the ith �i=1,2, . . . ,m� component LDPC

ode, and n denotes the codeword length, which is theame for all LDPC codes. The use of different LDPCodes allows us to optimally allocate the code rates. Ifll component LDPC codes are identical, the corre-ponding scheme is commonly referred to as the bit-nterleaved coded modulation (BICM). The outputs of

LDPC encoders are written row-wise into a block-nterleaver block. The mapper accepts m bits at timenstance i from the �mn� interleaver column-wisend determines the corresponding M-ary �M=2m� sig-al constellation point ��I,i ,�Q,i� in a two-dimensional

2D) constellation diagram such as M-ary PSK or-ary QAM. (The coordinates correspond to in-phase

nd quadrature components of M-ary 2D constella-ion.) The OFDM symbol is generated as described be-

0 2 4 6 8 10 120.0

0.2

0.4

0.6

0.8

1.0

|hxy||hxx|

Magnitude

Normalized frequency, f �

�=�/2, �=0

0 2 4 6 8 10 120.0

0.2

0.4

0.6

0.8

1.0

|hxy||hxx|

Magnitude

Normalized frequency, f �

�=�/3, �=0

(a)

(b)

ig. 1. (Color online) Magnitude response of hxx and hxy Jones ma-rix coefficients against the normalized frequency for (a) �=� /2 and=0, and (b) �=� /3 and �=0.

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low. NQAM input QAM symbols are zero-padded to ob-tain NFFT input samples for inverse FFT (IFFT) (thezeros are inserted in the middle rather than at theedges), and NG non-zero samples are inserted to cre-ate the guard interval. For efficient chromatic disper-sion and PMD compensation, the length of the cycli-cally extended guard interval should be longer thanthe total spread due to chromatic dispersion and themaximum value of DGD. The cyclic extension is ob-tained by repeating the last NG /2 samples of the ef-fective OFDM symbol part (NFFT samples) as a prefixand repeating the first NG /2 samples as a suffix. AfterD/A conversion (DAC), the OFDM signal is convertedinto the optical domain using the dual-drive Mach–Zehnder modulator (MZM). Two MZMs are needed,one for each polarization. The outputs of MZMs arecombined using the polarization beam combiner(PBC). The same DFB laser is used as a CW source,with x- and y-polarization being separated by a polar-ization beam splitter (PBS). Given the fact that thecomplexity of the MLC scheme is high for high speedimplementation, the BICM is adopted in the rest ofthe paper.

(

S/P converterand

Subcarrier mapperIFFT…

QAMsymbols

Sourcechannels

1

m

.

.

.

BlockInterleavermxn

Mapperm

LDPC encoderr1=k1/n… TLDPC encoder

rm=km/n

.

.

.

�/2

PBS

LocalDFB

FromSMF

PBS

Coherentdetector

ADC

ADC

LPF

LPF

Coherentdetector

ADC

ADC

LPF

LPF

Cyclicextensremov

Cyclicextensremov

Fig. 2. (Color online) The architecture of the polarization-multiplextransmitter architecture (x- or y-polarization), (c) receiver architectufeedback laser; PBS(C), polarization beam splitter (combiner); MZMLLRs, log-likelihood ratios.

The 100 Gb/s aggregate data rate can be achieveds follows. By setting the OFDM signal bandwidth to0 GHz and by employing the polarization multiplex-ng and 32-QAM we can achieve 100 Gb/s, with apectral efficiency of 10 bits/s /Hz. Another optionould be to use 16-QAM, but setting the OFDM signalandwidth to 12.5 GHz. However, the spectral effi-iency would be smaller �8 bits/s /Hz�. Both optionsmploy mature 10 Gb/s technology while achievinghe aggregate rate of 100 Gb/s. The operations of alllocks, except the symbol detector shown in Fig. 2(c),re similar to those we reported in [1,10], and forore details on OFDM with coherent detection an in-

erested reader is referred to an excellent tutorial pa-er due to Shieh et al. [7]. Here we describe the opera-ion of the symbol detector block, the calculation ofymbol log-likelihood ratios (LLRs), and the calcula-ion of bit LLRs, in the presence of laser phase noise.y re-writing Eq. (3) in scalar form we obtain, by ig-oring the laser phase noise at the moment to keephe explanation simpler,

r = h �k�s + h �k�s + n , �4�

Cyclic extensioninsertion

LPF

LPF

DAC

DAC

I

Q

sOFDM,y

To SMFDFB

MZMMZM

PBSFDMsmitters

sOFDM,x

PBC

Coherent detector

rI

rQ

APPDemapper

BitLLR

sCalculation

LDPC Decoder 1

LDPC Decoder m

1

m

.

.

.

FFTSymboldetection

FFT

… …

… …

DPC-coded OFDM scheme: (a) transmitter architecture, (b) OFDMand (d) balanced coherent detector configuration. DFB, distributedual-drive Mach–Zehnder modulator; APP, a posteriory probability;

(a)

b)

Oran

(c)

(d)

ional

ional

ed Lre,, d

x,i,k xx x,i,k xy y,i,k x,i,k

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ry,i,k = hyx�k�sx,i,k + hyy�k�sy,i,k + ny,i,k, �5�

where index k denotes the kth subcarrier, index i de-notes the ith OFDM symbol, hij�k��i , j� �x ,y� are thechannel coefficients due to PMD introduced by Eq. (1),sx,i,k and sy,i,k denote the transmitted symbols in x-and y-polarization, respectively, and corresponding re-ceived symbols are denoted by rx,i,k and ry,i,k. In Eqs.(4) and (5) nx,i,k and ny,i,k denote the ASE noise pro-cesses in x- and y-polarization. The equivalent chan-nel model is shown in Fig. 3, and it is consistent withprevious literature [6,7]. In the absence of ASE noise,Eqs. (4) and (5) represent the system of linear equa-tions with two unknowns sx,i,k and sy,i,k. By multiply-ing Eq. (4) with hxx�k� / �hxx�k��2 and Eq. (5) withhyy�k� / �hyy�k��2, the unknown transmitted symbols canbe estimated by

sx,i,k� =

hxx* �k�

�hxx�k��2�rx,i,k −hxy�k�hyy

* �k�

�hyy�k��2ry,i,k�

1 −hxx

* �k�hxy�k�

�hxx�k��2hyx�k�hyy

* �k�

�hyy�k��2

, �6�

sy,i,k� =hyy

* �k�

�hyy�k��2ry,i,k −

hyx�k�hyy* �k�

�hyy�k��2sx,i,k� , �7�

where sx,i,k� and sy,i,k� denote the detector estimates ofsymbols sx,i,k and sy,i,k transmitted on the kth subcar-rier of the ith OFDM symbol. Notice that the OFDMscheme with polarization diversity [7], assuming thatboth polarizations are used on a transmitter side andequal-gain combining on a receiver side, is the specialcase of the symbol detector described by Eqs. (6) and(7). By setting sx,i,k=sy,i,k=si,k and using the symmetryof channel coefficients, the transmitted symbol can beestimated by

si,k� = �hxx* �k�rx,i,k + hxy

* �k�ry,i,k�/��hxx�k��2 + �hxy�k��2�.

.

.

.,i ks

,i kn� � � �CD PNj kk e � �� H

,i kr

1,i ks �

1,i k�n� � � �CD PNj kk e � �� H

1,i k�r

.

.

.

.

.

.,i ks

,i kn� � � �CD PNj kk e � �� H

,i kr

1,i ks �

1,i k�n� � � �CD PNj kk e � �� H

1,i k�r

.

.

.

Fig. 3. (Color online) Equivalent OFDM channel model. �CD�k� de-notes the phase distortion of the kth subcarrier due to chromaticdispersion.

In the presence of laser phase noise the symbol de-ector estimates are a function of the laser phase noiserocess:

sx,i,k� =

hxx* �k�e−j�PN

�hxx�k��2 �rx,i,k −hxy�k�hyy

* �k�

�hyy�k��2ry,i,k�

1 −hxx

* �k�hxy�k�

�hxx�k��2hyx�k�hyy

* �k�

�hyy�k��2

, �8�

sy,i,k� =hyy

* �k�e−j�PN

�hyy�k��2ry,i,k −

hyx�k�hyy* �k�

�hyy�k��2sx,i,k� . �9�

The detector soft estimates of symbols carried byhe kth subcarrier in the ith OFDM symbol, sx�y�,i,k� ,re forwarded to the a posteriori probability (APP)emapper, which determines the symbol LLRs x�y��s�f x- (y-) polarization by

x�y��s��PN� = −�R�sx��y�,i,k�� PN�� − R�QAM�map�s��2

2�2

−�I�sx��y�,i,k�� PN�� − I�QAM�map�s��2

2�2 ;

s = 0,1, . . . ,2nb − 1 �10�

here R�� and I�� denote the real and imaginary partsf a complex number, QAM denotes the QAM-onstellation diagram, �2 denotes the variance of anquivalent Gaussian noise process originating fromSE noise, and map�s� denotes a corresponding map-ing rule (Gray mapping rule is applied here). (nb de-otes the number of bits carried by the symbol.) No-ice that symbol LLRs in Eq. (10) are conditioned onhe laser phase noise sample �PN=�T−�LO, which is aero-mean Gaussian process (the Wiener–Lévy pro-ess [17]) with a variance of �PN

2 =2��T+��LO��t��T and ��LO are the corresponding laser linewidthsntroduced earlier). This comes from the fact that es-imated symbols sx�y�,i,k� are functions of �PN. To re-ove the dependence on �PN we have to average the

ikelihood function (not its logarithm), over all pos-ible values of �PN:

x�y��s� = log −�

�

ex�y��s��PN�1

�PN�2�e−�PN

2 /2�PN2

d�PN.

�11�

he calculation of LLRs in Eq. (11) can be performedy numerical integration. For the laser linewidthsonsidered in this paper it is sufficient to use the trap-zoidal rule, with samples of �PN obtained by pilot-ided channel estimation as explained in [6].

tlstmiglssG

ctoFa

Fdct


Let us denote by bj,x�y� the jth bit in an observedsymbol s binary representation b= �b1 ,b2 , . . . ,bnb

� forx- (y-) polarization. The bit LLRs required for LDPCdecoding are calculated from symbol LLRs by

L�bj,x�y�� = log

s:bj=0

exp�x�y��s�

s:bj=1

exp�x�y��s�. �12�

The jth bit LLR in Eq. (12) is calculated as the loga-rithm of the ratio of a probability that bj=0 and prob-ability that bj=1. In the numerator, the summation isdone over all symbols s having 0 at the position j.Similarly, in the denominator summation is per-formed over all symbols s having 1 at the position j.

The bit LLRs calculated by Eq. (12) are forwardedto the corresponding LDPC decoders, as shown in Fig.2(c). The LDPC decoders from Fig. 2(c) employ thesum-product-with-correction term algorithm. TheLDPC code used in this paper belongs to the class ofquasi-cyclic (array) codes of large girth �g�10� [14], sothat the corresponding decoder complexity is low com-pared to random LDPC codes, and does not exhibit theerror floor phenomenon in the region of interest infiber-optics communications ��10−15�.

III. EVALUATION OF THE PROPOSED CODED-MODULATIONSCHEME IN THE PRESENCE OF PMD

We are turning our attention to the evaluation ofthe proposed scheme. To illustrate the efficiency ofthis scheme, in Fig. 4 we show the constellation dia-grams for an aggregate rate of 100 Gb/s, correspond-ing to the M=32 QAM and the OFDM signal band-width of 10 GHz, before [see Fig. 4(a)] and after [seeFig. 4(b)] PMD compensation, assuming the worst-case scenario ��=� /2 ,�=0�. The symbol detectionscheme described above is able to completely compen-sate the first-order PMD with DGD of even 1200 ps.In Fig. 5 we show both the uncoded and LDPC-codedBER performance of the proposed scheme against thepolarization diversity OFDM scheme with coherentdetection, for different constellations sizes. The com-ponent LDPC code is based on the girth-10LDPC(16935,13550) code. For M=4 QAM (QPSK), theOFDM system parameters were chosen as follows: thenumber of QAM symbols NQAM=512, the oversam-pling is two times, OFDM signal bandwidth is set to10 GHz, and the number of samples used in cyclic ex-tension is NG=16. For other constellation sizes �M=16,32,64�, the OFDM system parameters were cho-sen as follows: the number of QAM symbols NQAM=2048, the oversampling is two times, OFDM signalbandwidth is set to 10 GHz, and the number ofsamples used in cyclic extension is NG=64. In simula-tions, for the polarization diversity OFDM scheme,

he same OFDM signal was transmitted over both po-arizations. For the fair comparison of different M-arychemes the OSNR on the x-axis is given per informa-ion bit, which is also consistent with the digital com-unication literature [15,16]. The code rate influence

s included in Fig. 5 so that the corresponding codingains are net effective coding gains. The averageaunch power per OFDM symbol is set to −3 dBm (andimilarly as in wireless communications [15,16] repre-ents the power per information symbol), and theray mapping rule is employed.For DGD of 1200 ps, the proposed scheme performs

omparable to the polarization-diversity OFDM inerms of BER (the corresponding curves overlap eachther), but has two times higher spectral efficiency.or example, the aggregate data rate for M=32 QAMnd polarization multiplexed coded-OFDM is

(a)

(b)

ig. 4. The constellation diagrams for M=32 QAM (the aggregateata rate is 100 Gb/s) after 1200 ps of DGD observing the worst-ase scenario (�=� /2, �=0) (a) before PMD compensation and (b) af-er PMD compensation.

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100 Gb/s, while the aggregate rate of polarization di-versity coded-OFDM scheme is 50 Gb/s.

The aggregate data rate of 100 Gb/s can also beachieved for single carrier systems based on 32-QAMand polarization diversity. However, to deal with PMDsomeone has to use maximum-likelihood sequence de-tection (MLSD) [4,9], turbo equalization [2,8], or thedigital filtering approach [11]. The detector complexityof the corresponding turbo equalization or MLSDschemes grows exponentially as DGD increases[mostly due to the complexity of the Bahl–Cocke–Jelinek–Raviv (BCJR) and Viterbi algorithms [2,8],and for DGD of 1200 ps it would require the trellis de-scription (see [2,8]) with too many states to be of prac-tical importance. The proposed scheme also outper-forms the scheme implemented by Nortel Networksresearchers [11], capable of compensating the rapidlyvarying first order PMD with peak DGD of 150 ps[11]. The receiver complexity of polarization multi-plexed coded-OFDM is comparable to that of thecoded-OFDM with polarization diversity. The net ef-fective coding gain increases as the constellation sizegrows. For M=4 QAM based polarization multiplexedcoded-OFDM the net effective coding gain is 8.36 dBat BER of 10−7, while for M=32 QAM based LPDC-coded OFDM (of aggregate data rate 100 Gb/s) thecoding gain is 9.53 dB at the same BER. The largernet effective coding gains are expected at lower BERs.The laser linewidths of the transmitting and local la-ser were set to 10 kHz, so that the PMD and ASEnoise are predominant effects. For the influence of thelaser phase noise on coherent OFDM systems an in-terested reader is referred to [18].

IV. CONCLUSION

We proposed a particular polarization multiplexedcoded-OFDM scheme suitable for use in beyond100 Gb/s optical transmission and 100 Gb/s Ether-

0 4 8 12 16 20

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1Bit-errorratio, BER

Optical SNR, OSNR [dB] (per information bit)

M=4, RD=40 Gb/s:UncodedLDPC-coded




Fig. 5. (Color online) BER performance of the proposed polariza-tion multiplexed coded-OFDM scheme, for DGD of 1200 ps and theworst-case scenario (�=� /2, �=0). RD denotes the aggregate datarate.

et. By selecting the OFDM signal bandwidth to be0 GHz, and by using 32-QAM and polarization mul-iplexing, the aggregate data rate of 100 Gb/s ischieved. The spectral efficiency of the proposedcheme is 10 bits/s /Hz. For the same system param-ters, the corresponding polarization diversity coded-FDM would have the aggregate rate of 50 Gb/s,hich is insufficient for 100 Gb/s Ethernet. Therefore,

he proposed coded-modulation scheme achieves theggregate rate of 100 Gb/s, while employing the ma-ure 10 Gb/s technology. The proposed coded-odulation scheme is insensitive to PMD, while in

orresponding single carrier systems the PMD intro-uces severe performance degradation. The results ofimulations indicate that even 1200 ps of DGD, in po-arization multiplexed coded-OFDM systems with ag-regate data rate of 100 Gb/s, can completely be com-ensated with negligible penalty. In contrast to theMD turbo equalization scheme whose complexityrows exponentially as DGD increases (due to the ex-onential increase in complexity of the BCJR algo-ithm [2,8]), the complexity of the proposed scheme isssentially independent on the level of DGD as long ashe guard interval is longer than the maximum DGD.e also describe how to determine the symbols’ log-

ikelihood ratios in the presence of laser phase noise.

ACKNOWLEDGMENT

his work is supported in part by the National Sci-nce Foundation under grant IHCS-0725405 and inart by NEC Laboratories America.

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UHttttsajc

ci


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Ivan B. Djordjevic is an Assistant Profes-sor of Electrical and Computer Engineeringat the University of Arizona, Tucson. Priorto this appointment in August 2006, he waswith the University of Arizona (as a Re-search Assistant Professor); the Universityof the West of England, Bristol, UK; theUniversity of Bristol, Bristol, UK; TycoTelecommunications, Eatontown, NJ, USA;the National Technical University of Ath-ens, Athens, Greece; and National Telecom-

munications Company “Serbia Telecom,” Nis, Serbia. He receivedB.S., M.S., and Ph.D. degrees in electrical engineering from the

niversity of Nis, Nis, Serbia, in 1994, 1997, and 1999, respectively.is current research interests include optical networks, error con-

rol coding, constrained coding, coded modulation, turbo equaliza-ion, OFDM applications, and quantum error correction. He directshe Optical Communications Systems Laboratory (OCSL) withinhe ECE Department at the University of Arizona. Dr. Djordjevicerves as an Associate Editor for Research Letters in Optics and asn Associate Editor for International Journal of Optics. Dr. Djord-evic is an author of more than 90 journal publications and over 70onference papers.

Lei Xu received the B.S. degree in geophys-ics from Peking University, Beijing, China,in 1997, the M.E. degree in electronic engi-neering from Tsinghua University, Beijing,in 2000, and the Ph.D. degree in electricalengineering from Princeton University,Princeton, NJ, in 2004. Since 2004, he hasbeen a Research Staff Member with NECLaboratories America, Princeton. His cur-rent research interests include advancedmodulation and coding schemes for optical

ommunications, optical signal equalization and compensation, andnnovative optical devices.

Ting Wang received the M.S. degree inelectrical engineering from the City Univer-sity of New York and the Ph.D. degree inelectrical engineering from Nanjing Univer-sity of Science and Technology, Nanjing,China. Since 1991, he has been with NECLaboratories America, Princeton, NJ, wherehe is currently the Department Head of op-tical networking research. He is the authoror coauthor of approximately 70 publica-tions and 30 U.S. patents.

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Beyond 100 Gb∕s Optical Transmission Based on Polarization Multiplexed Coded-OFDM With Coherent Detection