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Published in IET OptoelectronicsReceived on 29th October 2008Revised on 3rd March 2009doi: 10.1049/iet-opt.2008.0059

ISSN 1751-8768

Coded-orthogonal frequency divisionmultiplexing in hybrid optical networksI.B. Djordjevic Department of Electrical and Computer Engineering, University of Arizona, Tucson, AZ 85721, USA

E-mail: [email protected]

Abstract: Future Internet should be able to support a wide range of services containing large amount of multimedia over different network types at a high speed. The future optical networks will therefore be hybrid,composed of different single-mode bre (SMF), multi-mode bre (MMF) and free-space optical (FSO) links. Inthese networks, novel modulation and coding techniques are needed that are capable of dealing withdifferent channel impairments, be it in SMF, MMF or FSO links. The authors propose a coded-modulationscheme suitable for use in hybrid FSO bre-optics networks. The proposed scheme is based on polarisation-multiplexing and coded orthogonal frequency division multiplexing (OFDM) with large girth quasi-cyclic low-density parity-check (LDPC) codes as channel codes. The proposed scheme is able to simultaneously deal withatmospheric turbulence, chromatic dispersion and polarisation mode dispersion (PMD). With a proper designfor 16-quadrature amplitude modulation (QAM)-based polarisation-multiplexed coded-OFDM, the aggregatedata rate of 100 Gb / s can be achieved for OFDM signal bandwidth of only 12.5 GHz, which represents ascheme compatible with 100 Gb / s per wavelength channel transmission and 100 Gb / s Ethernet.

1 Introduction The transport capabilities of bre-optic communicationsystems have increased tremendously, primarily because of advances in optical devices and technologies, and haveenabled the Internet as we know it today with all itsimpacts on the modern society. In particular, dense wavelength division multiplexing (DWDM) became a viable, exible and cost-effective transport technology [19]. Optical communication systems are developing rapidly because of the increased demands on transmissioncapacity. For example, the network operators are already considering 100 Gb/ s per DWDM channel transmission[2]. The free-space optical (FSO) communication [1012]is the technology that can address any connectivity needs inoptical networks, be it in the core, edge or access. Inmetropolitan area networks (MANs), the FSO can be usedto extend the existing MAN rings; in enterprise, the FSOcan be used to enable local area network (LAN)-to-LANconnectivity and intercampus connectivity; and the FSO is

an excellent candidate for the last-mile connectivity [11]. The future optical networks will allow the integration of bre optics and FSO technologies, and will, therefore, have

different portions of network being composed of bre[either single-mode bre (SMF) or multi-mode bre(MMF)] and FSO sections. These hybrid optical networksmight have a signicant impact in both military andcommercial applications, when pulling the ground bre isexpensive and takes a long time for deployment. Given thefact that hybrid optical networks will contain both FSOand bre-optic sections, one has to study not only how todeal with atmospheric turbulence present in the FSOportion of the network, but also the inuence of bre non-linearities, PMD and chromatic dispersion in the bre-optic portion of the network.

In this paper, we propose a coded-modulation scheme that is able to simultaneously deal with atmospheric turbulence,chromatic dispersion and polarisation-mode dispersion(PMD) in future hybrid optical networks. Moreover, theproposed scheme supports 100 Gb/ s per DWDM channeltransmission and 100 Gb/ s Ethernet, while employing themature 10 Gb/ s bre-optics technology. The proposed

hybrid optical network scheme employs the orthogonalfrequency division multiplexing (OFDM) as themultiplexing and modulation technique, and uses the

IET Optoelectron. , 2010, Vol. 4, Iss. 1, pp. 1728 17doi: 10.1049/iet-opt.2008.0059 & The Institution of Engineering and Technology 2010

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low-density parity-check (LDPC) codes as channel codes. With a proper design for 16 quadrature amplitudemodulation (QAM)-based polarisation-multiplexed coded-OFDM, the aggregate data rate of 100 Gb/ s can beachieved for the OFDM signal bandwidth of only 12.5 GHz, which represents a scheme suitable for 100 Gb/s Ethernet. Note that arbitrary forward error correction(FEC) scheme can be used in proposed hybrid opticalnetwork. However, the use of large girth LDPC codes [2]leads to the channel capacity achieving performance.

We consider two scenarios: (i) the FSO channelcharacteristics are known on the transmitter side and (ii)the FSO channel characteristics are not known on thetransmitter side. In both scenarios, we assume that bre-optic channel properties are known on the receiver side,obtained by pilot-aided channel estimation. Given the fact that transmitter and receiver nodes might be connected

through several FSO and bre-optic links, and that FSOlink properties can vary signicantly during the day, it isreasonable to assume that FSO link channel conditions arenot known on the receiver side. In the presence of rain,snow and fog, we assume that an RF feedback channel isused to transmit the channel coefcients to the transmitter, which adapts the transmitted power and data rate according to the channel conditions.

The proposed scheme has many unique advantages:(i) demodulation, equalisation and decoding are jointly performed; (ii) it is able to operate in the presence of channel impairments over different optical links, be it inSMF, MMF or FSO, (iii) it has high-bandwidth efciency (even 10 bits/ s/ Hz), (iv) it is compatible with future100 Gb/ s Ethernet technologies; and (v) the employedcoded modulation provides excellent coding gains. We alsodescribe about how to determine the symbol reliabilities inthe presence of laser phase noise, and describe a particular channel inversion technique suitable for dealing with PMDeffects.

The paper is organised as follows. In Section 2 we describethe proposed hybrid optical network and the corresponding coded-modulation scheme. In Section 3 we describe thechannel model, whereas in Section 4 we describe thereceiver architecture and transmission diversity principle. InSection 5 we report numerical results, and some important conclusions are given in Section 6.

2 Description of the proposedhybrid optical network An example of a hybrid FSO bre-optic network is shownin Fig. 1a . This particular example includes inter-satellitelinks and connection to aircrafts. The bre-optic portion of

the network could be a part of already installed MAN or wide area network (WAN). The FSO network portionshould be used whenever pulling the ground bre is

expensive and/ or takes too much time for deployment,such as urban and rural areas, where the optical bre linksare not installed. The corresponding hybrid opticalnetworking architecture is shown in Fig. 1b . We canidentify three ellipses representing the core network, theedge network and the access network. The FSO links canbe used in both edge and access networks. The hybridoptical networks impose a big challenge to the engineers,because the novel signal processing techniques should bedeveloped, which would be able to simultaneously dealatmospheric turbulence in FSO links, and with chromaticdispersion, PMD and bre non-linearities in bre-opticlinks. One such coded-modulation technique is describedin the rest of this section. By using the retro-reectors theFSO systems can be applied even when there is no line of sight between the transmitter and the receiver.

The proposed coded-modulation scheme employs thecoded-OFDM scheme with coherent detection. Note that the coded-OFDM scheme with direct detection has already been proposed by the authors in [12], as a scheme that incombination with interleaving is able to operate under strong atmospheric turbulence. The use of coherent detection offers the potential of even 24 dB improvement over uncoded direct detection counterpart. One portion of improvement (10 13 dB) is comes from the fact that coherent detection can approach quantum-detection limit

easier than direct detection. The second portion (about 11 dB) comes from the use of large-girth LDPC codes[1, 2]. Let us now describe the operation principle of

Figure 1 Illustration of hybrid optical networking principlea A hybrid FSO bre-optic network exampleb Hybrid optical networking architecture

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coded-OFDM scheme with coherent detection employing both polarisations. Given the fact that the signal fromFig. 1 is going to be transmitted over the FSO links andover the bre-optic links, we use a particular polarisationmultiplexing capable of eliminating the inuence of PMD. The transmitter and the receiver shown in Fig. 2, to beused in hybrid optical network from Fig. 1, are able to

simultaneously deal with atmospheric turbulence, residualchromatic dispersion and PMD. The bit streamsoriginating from m different information sources areencoded using different (n, ki ) LDPC codes of code rater i ki / n. ki denotes the number of information bits of thei th (i 1, 2, . . . , m) component LDPC code, and ndenotes the codeword length, which is the same for all

Figure 2 Transmitter and receiver congurations for LDPC-coded OFDM hybrid optical system with polarisation multiplexingand coherent detectiona Transmitter architectureb OFDM transmitter architecturec Hybrid optical link exampled Receiver architecturee Coherent detector conguration. PBS / PBC


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LDPC codes. The use of different LDPC codes allows us tooptimally allocate the code rates. If all component LDPCcodes are identical, then the corresponding scheme iscommonly referred to as the bit-interleaved codedmodulation (BICM). The outputs of m LDPC encodersare written row-wise into a block-interleaver block. Themapper accepts m bits at time instance i from the (m n)interleaver column-wise and determines the corresponding M -ary ( M 2m) signal constellation point (f I ,i , f Q ,i ) in a two-dimensional (2D) constellation diagram such as M -ary phase-shift keying (PSK) or M -ary QAM. (Thecoordinates correspond to in-phase and quadraturecomponents of M -ary 2D constellation.)

The OFDM symbol is generated as described below. N QAM input QAM symbols are zero padded to obtain N FFT input samples for inverse fast Fourier transform(IFFT) (the zeros are inserted in the middle rather than at

the edges), and N G non-zero samples are inserted to createthe guard interval. For efcient chromatic dispersion andPMD compensation, the length of the cyclically extendedguard interval should be longer than the total spreadbecause of chromatic dispersion and maximum value of differential group delay (DGD). The cyclic extension isobtained by repeating the last N G / 2 samples of theeffective OFDM symbol part ( N FFT samples) as a prex,and repeating the rst N G / 2 samples as a sufx. After D/ A conversion (DAC), the OFDM signal is convertedinto the optical domain using the dual-drive MachZehnder modulators (MZMs). Two dual-drive MZMs areneeded, one for each polarisation. The outputs of MZMsare combined using the polarisation beam combiner (PBC). The same distributed feedback (DFB) laser is used as a CW source, with x - and y -polarisations being separated by a polarisation beam splitter (PBS).

The operations of all other blocks in the transmitter aresimilar to those we reported in [9, 12], and for more detailson OFDM with coherent detection an interested reader isreferred to an excellent tutorial paper by Shieh et al. [4].

The key idea of this proposal is to use the OFDM with a large number of subcarriers (in the order of thousands) so that the OFDM symbol duration becomes in order of ms, and by means of interleavers in the order of thousands overcome theatmospheric turbulence with temporal correlation in theorder of 10 ms. For the OFDM scheme to be capable of simultaneously compensating for chromatic dispersion andPMD, in addition to the atmospheric turbulence, the cyclicextension guard interval should be longer than the totaldelay spread because of chromatic dispersion and DGD, asindicated above.

The OFDM is also an excellent candidate to be used for multi-user access [known as OFDM access (OFDMA)]. In

OFDMA, subsets of subcarriers are assigned to individualusers. OFDMA enables time and frequency domainresource partitioning. In time domain, it can accommodate

for the burst trafc (packet data) and enables multi-user diversity. In frequency domain, it provides further granularity and channel-dependent scheduling. InOFDMA, different numbers of sub-carriers can beassigned to different users, in order to support differentiated quality of service (QoS). Each subset of sub-carriers can have different kinds of modulation formats, andcan carry different types of data. The differentiated QoScan be achieved by employing the LDPC codes of different error correction capabilities. The OFDMA, therefore,represents an excellent interface between wireless/ wirelineand optical technologies.

Because for high-speed signals a longer sequence of bits isaffected by the deep fade in the ms range due to atmosphericturbulence, we propose to employ the polarisationmultiplexing and large QAM constellations in order toachieve the aggregate data rate of R D 100 Gb/ s, while

keeping the OFDM signal bandwidth in the order of 10 GHz. For example, by using the polarisation-multiplexing and 16-QAM, we can achieve R D 100 Gb/ sfor a OFDM signal bandwidth of 12.5 GHz, resulting in a bandwidth efciency of 8 bits/ s/ Hz. Similarly, by using the polarisation multiplexing and 32-QAM we can achievethe same data rate (R D 100 Gb/ s) for a OFDM signalbandwidth of 10 GHz, with a bandwidth efciency of 10bits/ s/ Hz.

The receiver description requires certain knowledge of thechannel. In what follows, we assume that bre-optic channelcharacteristics are known on the receiver side, because thebre-optics channel coefcients can easily be determined by pilot-aided channel estimation. On the other hand, thehybrid optical network may contain different FSO andbre-optic sections, while the channel characteristics of theFSO link can change rapidly even during the day, it isreasonable to assume that FSO channel characteristics arenot known on the receiver side. The FSO transmitter canuse a retro-reector and a training sequence to sense theFSO channel. We will further describe two concepts: (i)the transmitter does not have any knowledge about theFSO link and (ii) the transmitter knows the FSO link properties. When the transmitter knows the FSO link properties, we can employ the transmitter diversity concept.Before resuming our description of the coded-OFDMreceiver, in the next section we provide more details about FSO and bre-optic channel models.

3 Description of the channelmodel A commonly used turbulence model assumes that the variations of the medium can be understood as individualcells of air or eddies of different diameters and refractive

indices. In the context of geometrical optics, these eddiesmay be observed as lenses that randomly refract the optical wave front, generating a distorted intensity prole at the


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symbol and kth subcarrier can be represented by

r i ,k a i (k)e jf Y H (k) si ,ke

jf CD (k)e jf PN n i ,k (9) where si ,k [s x ,i ,k s y ,i ,k]

T denotes the transmitted symbol

vector, n

i ,k

[nx ,i,k n y ,i,k] T

denotes the noise vector becauseof the amplied spontaneous emission (ASE) and the Jones matrix H was introduced in (8). Here we use index kto denote the kth subcarrier frequency v k. f CD (k) denotesthe phase distortion of the kth subcarrier because of chromatic dispersion. f PN denotes the phase noise processf PN f T 2 f LO because of the laser phase noiseprocesses of transmitting laser f T and local laser f LO that are commonly modelled as the Wiener Le vy processes[15], which are a zero-mean Gaussian processes withcorresponding variances being 2p Dn Tjt j and 2p DnLO jt j, where Dn T and DnLO are the laser linewidths of transmitting and receiving laser, respectively. a i (k) denotesthe log-amplitude attenuation coefcient because of theatmospheric turbulence channel and f Y is the residualphase noise process that remained after modal-phasecompensation, as described above. From (9) we can createthe equivalent OFDM channel model as shown in Fig. 3.

4 Description of the receiver andtransmission diversity schemeIn this section we describe the operation of the receiver by observing two different transmission scenarios. In the rst scenario we assume that the transmitter does not have any knowledge about the FSO channel. In the second scenario we assume that the transmitter has knowledge about theFSO link, which is obtained by using the short training sequence transmitted towards the retro-reector. In bothscenarios we assume that the receiver knows the propertiesof the bre-optic portion of the network obtained by pilot-aided channel estimation. This can be achieved by organising the OFDM symbols in OFDM packets with

several initial OFDM symbols being used for channelestimation. Note that this approach is also effective inestimating the FSO channel properties in the regime of weak turbulence. The immunity to atmospheric turbulencecan be improved by employing the diversity approaches[16]. To maximise the receiver diversity, the multiplereceivers should be separated enough so that independency condition is satised. Given the fact that the laser beam isgetting expanded, during propagation it might not bepossible always to separate the receivers sufciently enoughso that the independence condition is satised. On theother hand, by using transmission diversity instead, theindependence condition is easier to satisfy. Moreover, it hasbeen shown in [17] that transmitter diversity performsbetter comparable to the maximum-ratio combining receiver diversity. In transmission diversity, the signal to betransmitted from the i th transmitter, characterised by pathgain r i exp[2 ju i ], is pre-multiplied by complex gain a i a i

exp[2 ju i ] (0 a i 1). On the receiver side, the weight a i that maximises the signal-to-noise ratio is chosen by [17]

a i r i

ffiffiffiffiffiffiPLi 1 r

2i q

where L is the number of transmitter branches. When thechannel is not known on the transmitter side, we have toset up a i to 1, and u i 0, and use the Alamouti-typescheme instead [16, 17]. Note, however, that the Alamouti-type receiver requires the knowledge of the FSOchannel, and as such is not considered here.

The operations of all blocks of receiver, except the symboldetector shown in Fig. 2d , are similar to those we reported in[9, 12]; for more details on OFDM with coherent detectionand chromatic dispersion compensation an interested reader is referred to [4]. Here we describe the operation of thesymbol detector block, the calculation of symbol log-likelihood ratios (LLRs) and the calculation of bit LLRs,in the presence of laser phase noise. By re-writing (9) inscalar form, we obtain, by ignoring the laser phase noise at the moment to keep the explanation simpler

r x ,i ,k a i (k)a i (k)e jf Y

hxx (k)s x ,i ,k hxy (k)s y ,i ,kh i nx ,i ,k (10)

r y ,i ,k a i (k)a i (k)e jf Y h yx (k)s x ,i ,k h yy (k)s y ,i ,kh i n y ,i ,k (11)

where we used the index k to denote the kth subcarrier, indexi to denote the i th OFDM symbol, hij (k) (i , j [ fx , y g) arethe channel coefcients because of PMD introduced by (8),s x ,i ,k and s y ,i ,k denote the transmitted symbols in x - and y -polarisation, respectively; whereas the corresponding received symbols are denoted by r x ,i ,k and r y ,i ,k. The weight a i is chosen in such a way so as to maximise the SNR, asexplained above. In (10) and (11) nx ,i,k and n y ,i,k denote the

ASE noise processes in x - and y -polarisation. In theabsence of ASE noise, (10) and (11) represent the systemof linear equations with two unknowns s x ,i ,k and s y ,i ,k, and

Figure 3 Equivalent OFDM channel model for hybrid optical networks


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upon solving we obtain

~ s x ,i ,k hxx = hxx

2 r x ,i ,k hxy h yy = h yy 2

r y ,i ,k 1 hxx hxy = hxx

2

h yx h yy = h yy

2

(12)

~ s y ,i ,k h yy

h yy 2 r y ,i ,k

h yx h yy

h yy 2

~ s x ,i ,k (13)

where ~ s x ,i ,k and ~ s y ,i ,k denote the detector estimates of symbolss x ,i ,k and s y ,i ,k transmitted on the kth subcarrier of i th OFDMsymbol. Note that the OFDM scheme with polarisationdiversity [4], assuming that both polarisations are used on a transmitter side and equal-gain combining on a receiver side, is the special case of the symbol detector described by (12) and (13). By setting s x ,i ,k s y ,i ,k s i ,k and using the

symmetry of channel coefcients, the transmitted symbolcan be estimated by

~ s i ,k hxx r x ,i ,k hxy r y ,i ,k

hxx 2 hxy

2

In the presence of laser phase noise the symbol detector estimates are function of the laser phase noise process

~ s x ,i ,k

(hxx = hxx 2)e jf PN r x ,i ,k (hxy h yy = h yy

2)r y ,i ,k

1 (hxx hxy = hxx 2)(h yx h yy = h yy 2

)

(14)

~ s y ,i ,k h yy e

jf PN

h yy 2 r y ,i ,k

h yx h yy

h yy 2

~ s x ,i ,k (15)

The detector soft estimates of symbols carried by thekth subcarrier in the i th OFDM symbol, ~ s x ( y )i ,k, areforwarded to the a posteriori probability (APP) demapper, which determines the symbol LLRs l x ( y )(s ) of x - ( y -)polarisation by

l x ( y ) s jf PN

Re ~ s i ,k,x ( y )(f PN)h iRe QAM(map(s )) 2

2s 2

Im ~ s i ,k,x ( y )(f PN)h iIm QAM(map(s )) 2

2s 2

s 0, 1, . . . , 2nb 1 (16) where Re[] and Im[] denote the real and imaginary parts of a complex number, QAM denotes the QAM-constellationdiagram, s 2 denotes the variance of an equivalent Gaussian

noise process originating from ASE noise and map(s )denotes a corresponding mapping rule (Gray mapping ruleis applied here). (nb denotes the number of bits carried by a symbol.) Note that symbol LLRs in (16) are conditionedon the laser phase noise sample f PN f T 2 f LO , whichis a zero-mean Gaussian process (the WienerLe vy process[15]) with variance s 2PN 2p (Dn T DnLO )jt j (Dn T andDnLO are the corresponding laser linewidths introducedearlier). This comes from the fact that estimated symbols~ s x ( y )i ,k are functions of f PN . To remove the dependence onf PN, we have to average the likelihood function (not itslogarithm), overall possible values of f PN

l x ( y )(s ) log 1

1

exp l x ( y ) s jf PN h i 1

s PN ffiffiffiffi2p p (exp

f 2PN

2s 2PN !df

PN)(17)

The calculation of LLRs in (17) can be performed by numerical integration. For the laser linewidths consideredin this paper it is sufcient to use the trapezoidal rule, withsamples of f PN obtained by pilot-aided channel estimationas explained in [4].

Let us denote by b j ,x ( y ) the j th bit in an observed symbol s binary representation b (b 1 , b 2 , . . . , b nb ) for x - ( y -)polarisation. The bit LLRs required for LDPC decoding are calculated from the symbol LLRs by

L(^b j ,x ( y )) log Ps :b j 0 exp l x ( y )(s )h iPs :b j 1 exp l x ( y )(s )h i

(18)

Therefore the j th bit LLR in (18) is calculated as thelogarithm of the ratio of a probability that b j 0 andb j 1. In the nominator, summation is performed over allsymbols s having 0 at the position j . Similarly, in thedenominator summation is performed over all symbols s having 1 at the position j . The bit LLRs calculated by (18) are forwarded to the corresponding LDPC decoders. The LDPC decoders from Fig. 2d employ the sum-product-with-correction term algorithm. The LDPC codeused in this paper belong to the class of quasi-cyclic(array) codes of large girth ( g 10) [2, 18], so that thecorresponding decoder complexity is low compared torandom LDPC codes, and do not exhibit the error oor phenomena in the region of interest in bre-opticscommunications ( 102 15 ).

The parity check-matrix H of quasi-cyclic (QC) ( N , K )LDPC codes [18] considered in this paper can be


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represented by

H

I I I . . . I I P S [1] P S [2] . . . P S [c 1]

I P 2S [1] P 2S [2] . . . P 2S [c 1]. . . . . . . . . . . . . . .

I P (r 1)S [1] P (r 1)S [2] . . . P (r 1)S [c 1]

266664

377775 where I is the p p ( p is a prime number) identity matrix, P

is the p p permutation matrix ( p i ,i 1 p p ,1 1, i 1, 2,. . . , p 2 1; other elements of P are zeros), whereas r and crepresent the number of rows and columns, respectively. The set of integers S are to be carefully chosen from the set

f0, 1, . . . , p 2 1g so that the cycles of short length, incorresponding Tanner (bipartite) graph representation of the parity-check matrix, are avoided. A bipartite (Tanner)graph is a graph whose nodes may be separated into twoclasses (variable and check nodes), and where undirected

edges may only connect two nodes not residing in the sameclass. The Tanner graph of a code is drawn according tothe following rule: check (function) node c is connected to variable (bit) node v whenever element hcv in a parity-check matrix H is a 1. There are N -K check nodes and N variablenodes. As an illustrative example, consider the H -matrix of the following LDPC code

H 1 0 1 0 1 01 0 0 1 0 10 1 1 0 0 10 1 0 1 1 0

26643775

For any valid codeword v [v 0 v 1 . . . v N 2 1], the checks usedto decode the codeword are written as

Equation (c 0): v 0 v 2 v 4 0 (mod 2) Equation (c 1): v 0 v 3 v 5 0 (mod 2) Equation (c 2): v 1 v 2 v 5 0 (mod 2) Equation (c 3): v 1 v 3 v 4 0 (mod 2)

The bipartite graph (Tanner graph) representation of thiscode is given in Fig. 4a . The circles represent the bit (variable) nodes, whereas the squares represent the check (function) nodes. For example, the variable nodes v 0 , v 2 andv 4 are involved in equation (c 0), and therefore connected tothe check node c 0 . A closed path in a bipartite graphcomprising l edges that closes back on itself is called a cycleof length l . The shortest cycle in the bipartite graph is calledthe girth. The girth inuences the minimum distance of LDPC codes, correlates the extrinsic LLRs and thereforeaffecting the decoding process. The use of large girthLDPC codes is preferable because the large girth increasesthe minimum distance, and de-correlates the extrinsic info

in the decoding process. To check for the existence of short cycles, one has to search over H -matrix for the patternsshown in Figs. 4b and c . The codeword length is determined

by N jS j p , where jS j denotes the cardinality of set S , andthe code rate is lower bounded by (1-r / jS j). For example, by selecting p 1123 and S f0, 2, 5, 13, 20, 37, 58, 91, 135,160, 220, 292, 354, 712, 830g an LDPC code of rate 0.8,girth g 10, column weight 3 and length N 16 845 isobtained. For more details on LDPC codes an interestedreader is referred to an excellent book by MacKay [19].

5 Evaluation of the proposedhybrid optical network We are turning our attention to the evaluation of theproposed hybrid optical network. We rst compare theBER performance of the employed girth-10 LDPC codesagainst RS codes, concatenated RS codes, turbo-product codes (TPCs) and other classes of LDPC codes. Theresults of simulations for an additive white Gaussian noise(AWGN) channel model are given in Fig. 5. The girth-10LDPC(24015,19212) code of rate 0.8 outperforms the

concatenation RS(255,239)RS(255,223) (of rate 0.82) by 3.35 dB and RS(255,239) by 4.75 dB, both at BER of 10

2 7. The same LDPC code outperforms projective

Figure 4 Identication of short cycles in bipartite graphrepresentation of a parity-check matrix a Bipartite graph of LDPC(6,2) code described by H matrix above.Cycles in a Tanner graphb Cycle of length 4c Cycle of length 6


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geometry (PG) (2,26)-based LDPC(4161,3431) (of rate0.825) of girth-6 by 1.49 dB at a BER of 102 7, andoutperforms girth-8 LDPC(4320,3242) of rate 0.75 by

0.25 dB. At a BER of 102 10

it outperforms lattice-based

LDPC(8547,6922) of rate 0.81 and girth-8 by 0.44 dB,and BCH(128,113)xBCH(256,239) TPC of rate 0.82 by 0.95 dB. The net effective coding gain at aBER of 102 12 is

10.95 dB.

Figure 5 Large girth QC LDPC codes against RS codes, concatenated RS codes, TPCs, and previously proposed LDPC codes

Figure 6 The constellation diagrams for polarisation-multiplexed 16-QAM (the aggregate data rate is 100 Gb / s) after 500 psof DGD for s X 0.1, s Y 0.05 and OSNR 50 dB observing the worst case scenario ( u p / 2 and 1 0) without transmission diversity a Before PMD compensationb After PMD compensation. The corresponding constellation diagrams in the presence of PMD only (for DGD of 500 ps)c Before PMD compensationd After PMD compensation


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In the simulation results shown in Figs. 6 and 7 we assumethat PMD channel coefcients are known at the receiver,because they can easily be determined by pilot-aidedchannel estimation [3, 4]. On the other hand, the FSOchannel may change signicantly during the day time, andas such is difcult to estimate. To illustrate the efciency of this scheme, in Figs. 6a and b we show the constellationdiagrams for an aggregate rate of 100 Gb/ s, corresponding to the M 16 QAM and the OFDM signal bandwidth of 12.5 GHz in the presence of atmospheric turbulence(s X 0.1 and s Y 0.05), before (see Fig. 6a ) and after (see Fig. 6b ) PMD compensation, assuming the worst-casescenario (u p / 2 and 1 0). The corresponding constellation diagrams in the presence of PMD only areshown in Figs. 6c and d . The proposed coded-modulationscheme is able to compensate for the PMD with DGD of even 500 ps in the presence of atmospheric turbulencecharacterised by s X 0.1 and s Y 0.01.

In Fig. 7 we show the BER performance of the proposedscheme for both uncoded case (Fig. 7a ) and LDPC-codedcase (Fig. 7b ). The OFDM system parameters were chosenas follows: the number of QAM symbols N QAM 4096,the oversampling is two times, the OFDM signalbandwidth is set to either 10 GHz ( M 32) or 12.5 GHz ( M 16) and the number of samples used in cyclicextension N G 64. For the fair comparison of different M -ary schemes the optical signal-to-noise ration (OSNR)on the x -axis is given per information bit, which is alsoconsistent with digital communication literature [20]. Thecode rate inuence is included in Fig. 7 so that thecorresponding coding gains are net-effective coding gains. The average launch power per OFDM symbol is set to-3 dBm (and similarly as in wireless communications [20]represents the power per information symbol), and theGray mapping rule is employed. To generate thetemporally correlated samples according to (6), we used the

Figure 7 BER performance of the proposed hybrid optical network scheme

a Uncoded BER curvesb LDPC-coded BERsRD Denotes the aggregate data rate and BOFDM is the OFDM signal bandwidth. TD i : transmission diversity of order i


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LevinsonDurbin algorithm [21]. From Figs. 6 and 7 it canbe concluded that PMD can be successfully compensatedeven in the presence of atmospheric turbulence. The most of degradation is coming from the FSO channel, as shownin Figs. 6 and 7. The 32-QAM case with aggregate data rate R D 100 Gb/ s performs 1.9 dB (at BER 10

2 6) worse than 16-QAM (with the same aggregate rate)although the occupied bandwidth is smaller.

The net coded gain improvement (at BER of 102 6) of LDPC-coded OFDM over uncoded OFDM is between11.05 dB ( M 16, s X 0.01, s Y 0.01, corresponding to the weak turbulence regime) and 11.19 dB ( M 16,s X 0.1, s Y 0.01, corresponding to the mediumturbulence regime). The additional coding gainimprovement because of transmission diversity with twolasers is 0.19 dB for 32-QAM-based OFDM (s X 0.01and s Y 0.1) at a BER of 10

2 6. On the other hand, the

improvement due to transmission diversity for the uncodedcase (at the same BER) is 1.26 dB. Therefore in the regimeof weak atmospheric turbulence, the improvements due totransmission diversity are moderate. On the other hand, inthe moderate turbulence regime the use of transmissiondiversity is unavoidable. Otherwise, the uncoded BER error oor is so high (see s X 0.5, s Y 0.1 curve in Fig. 7a )that even the best LDPC codes are not able to handle, if the complexity is to be kept reasonably low. Withtransmission diversity, in moderate turbulence regime, weobtain BER performance comparable to the case in theabsence of turbulence regime, as shown in Fig. 7. Thestrong turbulence regime is not considered here because of the lack of an appropriate temporal correlation model. (Theatmospheric turbulence model described in Section 3 is not a valid model in the strong turbulence regime.)

The laser linewidths of transmitting and local laser were set to 10 kHz, so that the atmospheric turbulence, PMD and ASE noise are predominant effects. For the inuence of laser phase noise on coherent OFDM systems, aninterested reader is referred to [22]. Note that BER threshold required to achieve BER 10

2 6 at the output of the LDPC decoder is 1.96 102 2, and in this regionBER values for different laser linewidths are comparable.

6 Conclusion We proposed a particular polarisation-multiplexed coded-OFDM scheme suitable for use in hybrid FSO bre-optics networks. This scheme is able to simultaneously deal with atmospheric turbulence, chromatic dispersion andPMD. We show that PMD can be compensated even inthe presence of atmospheric turbulence. We have foundthat the most of the degradation comesfrom FSO channel. The proposed coded-modulation scheme supports 100 Gb/s per wavelength transmission and 100 Gb/ s Ethernet. We

compare the BER performance of two schemes with a xedaggregate rate of 100 Gb/ s. The rst scheme employs 32-QAM and occupies 10 GHz (with a bandwidth efciency

of 10 bits/ s/ Hz), whereas the second scheme employs 16-QAM and occupies 12.5 GHz (with bandwidth efciency of 8 bits/ s/ Hz). We have found that the 16-QAM schemeoutperforms 32-QAM by 1.9 dB at a BER of 10

2 6,although it has a higher bandwidth, because larger constellation schemes are more sensitive to the atmosphericturbulence. The net coded gain improvement (dened at a BER of 10

2 6) of LDPC-coded 16-QAM OFDM, for s X 0.1 and s Y 0.01, over uncoded-OFDM 11.19 dB. The improvements because of transmission diversity aremoderate in weak turbulence, and signicant in moderateturbulence regime.

7 Acknowledgment This work was supported in part by the National ScienceFoundation (NSF) under Grant IHCS-0725405.

8 References

[1] MINKOV L.L., DJORDJEVIC I.B., BATSHON H.G., E T AL.:Demonstration of PMD compensation by LDPC-codedturbo equali zation and channel capaci ty losscharacterization due to PMD and quantization, IEEE Photon. Technol. Lett. , 2007, 19 , pp. 18521854

[2] DJORDJEVIC I.B., MINKOV L.L., BATSHON H.G.: Mitigation of linear and nonlinear impairments in high-speed opticalnetworks by using LDPC-coded turbo equalization, IEEE J. Sel. Areas Commun. , 2008, 26 , pp. 7383

[3] SHIEH W., YI X., MA Y., TANG Y.: Theoretical and experimentalstudy on PMD-supported transmission using polarizationdiversity in coherent optical OFDM systems, Opt. Express ,2007, 15 , pp. 99369947

[4] SHIEH W., YI X., MA Y., YANG Q.: Coherent optical OFDM: hasits time come? [Invited], J . Opt. Netw. , 2008, 7,pp. 234255

[5] ALIC N., PAPEN G.C., SAPERSTEIN R.E., ET AL.: Experimentaldemonstration of 10 Gb / s NRZ extended dispersion-limited reach over 600 km-SMF link without opticaldispersion compensation. Proc. OFC / NFOEC 2006, March2006, Paper OWB7

[6] POGGIOLINI P., BOSCO G., SAVORY S., BENLACHTAR Y., KILLEY R.I.,PRAT J.: 1,040 km uncompensated IMDD transmission overG.652 ber at 10 Gbit / s using a reduced-state SQRT-metric MLSE receiver. Proc. ECOC 2006, Cannes, France,September 2006, PDP Th4.4.6

[7] SUN H., WU K.-T., ROBERTS K.: Real-time measurements of a40 Gb / s coherent system, Opt. Express , 2008, 16 ,pp. 873879


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