optical fiber code-division multiple-access networks using concatenated codes

170 JOURNAL OF COMMUNICATIONS AND NETWORKS, VOL. 4, NO. 3, SEPTEMBER 2002

Optical Fiber Code-Division Multiple-Access NetworksUsing Concatenated Codes

Pham Manh Lam and Do Quang Minh

Abstract: An optical fiber code-division multiple-access (CDMA)network is proposed in which encoding is based on the use of con-catenated sequences of relatively large weight. The first short com-ponent sequence in the concatenated sequence permits realisticelectronic encoding of each data bit. The chips of this sequenceare then all-optically encoded at substantially higher rate. In spiteof the relatively large weight of the sequence the all-optical encoderis practical by virtue of the shortness of the component sequences.The use of Gold and Lempel sequences as component sequences forgenerating the concatenated sequences is studied and the bit-errorrate (BER) performance of the proposed system is presented as afunction of the received optical power with the number of simulta-neous users as parameter.

Index Terms: Optical CDMA, CDMA networks, concatenatedcodes.

I. INTRODUCTION

Code-division multiple-access has been extensively studiedfor satellite and mobile-radio applications and more recently, foruse in wireless local-area networks (LANs). As is well known,in order to accommodate a large number of users on CDMAnetworks, long sequences requiring large transmission band-widths are needed, placing serious limits on radio channels andmetallic transmission lines. For this reason, incoherent opticalcode-division multiple-access (OCDMA) over single-mode op-tical fibers holds out the promise of allowing the use of very longsequences. In recent years, many different schemes have beenproposed for incoherent OCDMA networks. The first approachuses sequence-inversion keying (SIK) of large-weight unipolarsequences (a large number of “1s” in the sequence) and at thereceiver the unipolar sequences are correlated with the bipolarform of the unipolar reference sequence [1]–[4]. Since large-weight codes can be used, the number of available sequencesand hence the number of potential network subscribers is large.However, if relatively long sequences were used, the optical re-combination loss rapidly becomes a serious limitation [1], [2]or the synchronous switching at the chip rate [3] is requirednegating a major advantage of all-optical processing. The sec-ond approach relies on low-weight codes and unipolar-unipolarcorrelation [5], [6]. Because the correlation is based on powersummation, compared to the conventional bipolar codes of sim-

Manuscript received December 11, 2000; approved for publication by H. Vin-cent Poor, Division I Editor, May 23, 2001.

P. M. Lam is with Department of Telecommunication Science, Faculty ofScience and Technology, Assumption University, Bangkok, Thailand, e-mail:[email protected].

D. Q. Minh is with Department of Computer Science, Faculty of Science andTechnology, Assumption University, Bangkok, Thailand, e-mail: [email protected].

Laser

LL -1

LL - 2

L1

L0

4Tc

LTc

LTc

2LTc

. . .

Inner SequenceSelector

Outer SequenceGenerator

DataSource

Lattices... Output

InnerEncoder

Electrical signal

Optical signal

4Tc

L=(N1+2)/4

Fig. 1. Transmitter for optical fiber CDMA networks.

ilar length these unipolar codes yield a lower ratio of the auto-correlation peak to the maximum value of the cross-correlation,and are therefore prone to higher multiple-access interference.This leads to a serious degradation in the bit error probability(BER) as the number of simultaneous users increases and thedegradation can not be overcome even for arbitrary high opticalpower.

From the foregoing we conclude that for large networks anew strategy is required that would allow the use of large-weightcodes but would avoid electronic processing at the chip rate. Inthis paper we propose the use of concatenated sequences formedby the Kronecker product [7] of two sequences of relativelylarge weight: Gold [8] and Lempel sequences [9], in incoherentoptical fiber CDMA systems. The transmitter and receiver ofthe proposed network are described and the analysis of the BERperformance of the system is presented. The BER is comparedto that of another optical CDMA system. We find that, besidesbeing practical the proposed system permits a large number ofsimultaneous users.

II. TRANSMITTER AND RECEIVER

Let �� and �� denote unipolar sequences of length�� and ��, respectively. The sequence �� of length� � �� is a concatenated sequence made up of the innersequence �� and the outer sequence �� if each “1”chip of �� is encoded by another sequence �� andeach “0” chip of �� is replaced by ��

�� which is the

complement of �� [7].In the proposed system, the inner sequences consist of unipo-

lar balanced Gold sequences generated by encoding each “1”chip of Gold sequences [8] by two chips “10” and each “-1”chip of the sequences by “01”. The outer sequences are Lem-pel sequences, which are unipolar balanced sequences and can

1229-2370/02/$10.00 c� 2002 KICS

LAM AND MINH: OPTICAL FIBER CODE-DIVISION MULTIPLE-ACCESS NETWORKS... 171

Comparator

Integrator

Outer ReferenceSequence Generator

ClockRecovery

From Star

Coupler

+

+

_

A

B

ThresholdAdjust

Divider(by N2)

DelayAdjust

SynchronisationCircuit

Output

Electronic SwitchesOuter Correlator

OpticalInner

Correlator

Detector

Fig. 2. Receiver for optical fiber CDMA networks.

be generated by a simple algorithm [9]. The spreading is im-plemented by sequence-inversion keying (SIK) whereby, each“1” data bit is replaced by a unipolar outer sequence while thecomplement of the sequence replaces each “0” bit. Each “1”chip of the outer sequence is represented by a unipolar innersequence while the complement of this sequence is used foreach “0” chip of the outer sequence. It has been shown in [2]that a balanced Gold sequence of length �� can be broken into� � �� blocks, where the first �� blocks consist offour chips and the last block consists of two chips. The 4-chipcombinations �� and the 2-chip combina-tions �� can be generated with a 2-stage programmable op-tical lattice consisting of one 3dB-coupler and two �� electro-optic switches that can be switched from a 3dB-split state to thebar-state or cross state. Those lattices can be used to constructthe transmitter as shown in Fig. 1. In this transmitter, outer se-quences are electronically generated by the outer sequence gen-erator and used to control the inner sequence selector. The lasergenerates a train of optical pulses of maximum pulse width � �at the rate �� where �� is the chip duration of theconcatenated sequences, � is the bit duration and �� is the chip duration of the outer sequences. The train of opti-cal pulses is directed to the inner encoder where inner balancedGold sequences are generated. This encoder is a parallel delay-line encoder consisting of �� branches providing delays�� and each branch is connected to a lat-tice The inner sequence selection can be realized by controllingthe setting of lattices �� so that thelattice can generate the �th block of the inner sequence. Whenthere is a change from “1” to “0” or “0” to “1” in the outersequence, the inner sequence selector generates signals for re-setting each lattice allowing the inner encoder to generate com-plement sequences. Thus, the transmitter can be programmableto generate any sequence of the concatenated code.

The receiver structure is shown in Fig. 2 and consists of anoptical inner correlator of the same structure as the inner en-coder described above and an electronic outer correlator. In thisreceiver, the optical output of the inner correlator is convertedinto an electrical current in an avalanche photodiode (APD). Af-ter amplification this signal is fed to the outer correlator whereit is split into two branches: One is to the synchronization cir-cuit and the other is to two electronic switches � and �, whichare switched by the outer reference sequence and its comple-ment, respectively. These sequences are generated by the outerreference sequence generator, which is controlled by the syn-

chronization circuit. The outputs of the switches are subtractedand the resulting signal is then integrated over a bit duration,sampled and detected with reference to zero threshold. The syn-chronization circuit is based on the detection of the peaks of the“inner” auto-correlation between the desired signal and the innerreference sequence. These peaks are detected by using a com-parator with adjustable threshold and used for clock recovery.

It should be noted that with sequence-inversion keying andusing the unipolar-bipolar correlator, the output of the receiveris equivalent to that of receivers used in bipolar radio CDMAsystems. This allows us to make use of well-known CDMAcodes published in the literature (Gold codes, Lempel codes,etc.) even though the encoding operation is based on opticalsequences only.

III. PERFORMANCE ANALYSIS

We investigate an optical fiber CDMA network with simul-taneous users. Each user is assigned a fixed sequence serving asits reference. A user wishing to transmit data encodes its data byusing the reference sequence of its intended receiver. The SIKoptical signal at the output of the �th transmitter �� can be written as

��

��

��

��

� �� (1)

where �� denotes the chip optical intensity of the �th user,�� and ��

�� are the code waveform and its complement,

and ��, ��

�� are the transmitted binary signal and its com-

plement, respectively. The term � �

�� is given by

��

��

��

�� (2)

where �� is the binary value �� of the data bit in the th bit interval of duration � , and �� is the unit amplitudeunipolar rectangular pulse of duration � . The waveforms � �

��

can be written as

��

��

��

�� (3)

where the sequence �� of length � is the reference se-quence of the intended receiver that is constructed from the innersequence �� of length�� and the outer sequence ��of length ��. �� is the unit amplitude unipolar rectangularpulse of duration �� . Assume that every user transmitsthe same chip optical power and the received chip optical poweris �� for all � and the simultaneous transmitters are not syn-chronized to each other. The total received optical signal � ��at the input of the �th receiver is the incoherent sum

��

��

��

��

��

��

� ��

(4)where �� is the transmission delay associated with the �th sig-nal. The inner correlation of the received optical signal to the


inner reference code waveform � �

�� produces the optical sig-nal �� at time � � �� , and �� can be writtenas

��

��

� ��

�

��

��

�� (5)

where � � �� is the optical recombination loss factorof the receiver and � �

�� is given by

� �

��

��

�� (6)

with �� being the inner reference sequence of the �th user.The resulting optical signal is converted into an electrical cur-rent in an APD of responsivity �� (at unit gain). Theelectrical signal is directed to the outer correlator that consistsof two switches: One is switched by the outer reference wave-form ��

�� and the other is switched by its complement � ��

with ��

�� being given by

��

��

��

�� (7)

and �� being the outer reference sequence of the �th user,and �� is the unit amplitude unipolar rectangular pulse ofduration ��. The current �� at the output of the integrator attime � � � is

��

��

�

��

� �

�

� �

��

��

� ��

�

��

��

��

��

��

�

��

��

�� (8)

where � is the APD gain and �� is the composite noise cur-rent composed of shot noise and thermal noise. For � � � � ��, we have

��

��

��

��

� � ��

��

� (9)

� �

��

� ��

�� (10)

Without loss of generality, we can normalize the delays to thedelay �� of the first transmitter and assume � � �� for� � � � �. Substitute (9) and (10) into (8) and note that bothcomponents of the concatenated sequences are balanced, (8) canbe rewritten in the short form

��

��

�� (11)

with

��

�� (12)

where �� denotes the data bit which can be either “1” or “-1”and

��

��

�

��

� �

�

� �

��

� ��

�

� � ��

��

�� (13)

(12) shows the desired signal and (13) represents the multiple-access interference (MAI) caused by the �th user at the receiverof the �th user. For large � and � , we may model all the MAIterms as a zero-mean Gaussian process. The variance of the totalMAI, derived in the Appendix, can be approximately calculatedby

��

��

�

�

��

��

��

�� (14)

where �� is the discrete aperiodic cross-correlation func-tion for sequences �� and ��. The shot noise inthe photodiode can be approximated by Gaussian statistics. Thevariance of the shot noise generated by the APD can be calcu-lated by [10]:

��

where � � �� is the electric charge, �� is themean value of the photo-current, �� is the dark current, � is thenoise-equivalent receiver bandwidth and �� is the excess noisefactor of the APD and is given by

��

where �� is the APD effective ionization ratio. The mean valueof photocurrent is

��

��

Therefore, the variance of the shot noise due to the APD can beevaluated to be

��

��

��

��

The thermal noise can be also modeled as a Gaussian randomprocess and the variance of the thermal noise is

��

��

where �� Æ� is the Boltzmann’s constant,�� is the receiver noise temperature and �� is the receiver loadresistor. By assuming all the noise processes to be independentthe total noise power is simply the sum of the variances

��

��

��

��

��

��

� (15)

The possible errors in the received bit stream occur at the de-tector which compares the input signal level to a preset thresholdlevel and issues a bit “1” or “0” depending on whether the sam-pled level is above or below the threshold, respectively. For theproposed optical fiber CDMA network the optimum detectionthreshold is zero and the BER is given by [10]:

��

�� !�

��

(16)


Table 1. Typical laser link parameters.

Name Symbol ValueAPD responsivity (at unit gain) � 0.84 A/WAPD gain � 100APD effective ionization rate �� 0.02APD dark current �� 1 nAReceiver load resistor �� 50 �Laser pulse width �� 0.03 nsReceiver noise temperature �� 300 Æ�

where �� and �� are the average values and the standarddeviations of the sampled currents for bits “1” and bit “0”, re-spectively; �� is the complementary error function, de-fined as

��

��

�

��

��

For the proposed system �� and �� , therefore, (16)can be written as

��

��

��

��

where �� is calculated using (12) with �� and ��

.

Finally, the BER can be approximated by:

��

��

��

��

� ��

��

IV. COMPARISON TO OTHER OCDMA SYSTEMS

We compare the proposed system with the incoherent opti-cal fiber CDMA system using optical orthogonal codes (OOCs),parallel delay line correlator with double hard-limiters and APD[6]. At first, it should be noted that the receiver for OOC se-quences is of fixed reference sequence (i.e., non-programmable)while the proposed receiver is fully programmable. The BERperformance of both systems is calculated as a function of thereceived chip optical power � � �� . Con-catenated sequences of length � � � generated from bal-anced Gold sequences of length �� as inner sequencesand Lempel sequences of length�� as outer sequences areused for the proposed receiver. In order to have a fair compar-ison both systems should use code sequences of approximatelysame lengths. Hence, we calculate the BER of the system usingOOC sequences of length � � �� and weight � � � usingequation (56) of [6]. The other parameters, which are the sameas those used in [6] are shown in Table 1. Note that both systemsoperate at a data bit rate of about 32.5 Mb/s because laser pulsewidth �� ns is used for both systems. It is found thatthe system using concatenated codes can support a maximumof 40 simultaneous users at �� whereas the systemsusing OOCs can support a maximum of 10 simultaneous usersat the same BER. This is illustrated in Fig. 3 where we show theBER versus the received chip optical power of two systems. Itcan be seen that for a �� and � � the proposed

Received chip optical power Ps (dBm)

BER

1

0.1

0.01

0.001

10-4

10-5

10-6

10-7

10-8

10-9

-50 -40 -30 -20 -10 0

Concatenated codesN=1008, N=14, K=10

Concatenated codesN=1008, N=14, K=40

OOCs N=1023, K=10

OOCs N=1023, K=40

Fig. 3. BER of the proposed receiver in comparison to the receiver usingOOCs.

system requires a chip optical power of -42 dBm while for thesystem using OOCs a higher chip optical power of -28 dBm isrequired. If the number of simultaneous users increases to 40the proposed system still can achieve �� with a re-ceived chip optical power of -24 dBm, while the performance ofthe system using OOCs is limited at�� . Concate-nated codes also provide a larger number of sequences in a set.There are 216 sequences in the set of concatenated sequencesof length � � � [4], while the maximum number of avail-able OOC sequences of length � � �� and weight � � � is�� [5].

V. CONCLUSIONS

We have proposed an optical fiber CDMA system in which theextensive signal-processing capabilities of electronics have beencombined with the high-speed capabilities of all-optical signalprocessing. The bit-error rate of the system in the presence ofnoise and multiple-access interference has been evaluated andcompared to the incoherent optical fiber CDMA system usingoptical orthogonal codes, parallel delay line correlator with dou-ble hard-limiters and APD. It has been found that the proposedsystem using concatenated codes can support a maximum of 40simultaneous users at �� whereas the systems us-ing OOCs can support a maximum of 10 simultaneous users atthe same BER. In addition, for the same number of simultane-ous users, the proposed system requires a lower received chipoptical power for achieving the same BER as that of the sys-tem using OOCs. Finally, concatenated codes provide a largernumber of sequences in a set of sequences of approximately thesame lengths. Therefore, the system using concatenated codescan have a larger number of potential subscribers.

APPENDIX

In this appendix, the variance of the total multiple access in-terference (MAI) at the receiver of the �th user is derived. Sincethe component sequences of concatenated sequences are bal-anced, (13) representing the MAI caused by the �th user at the


receiver of the �th user can be simplified and written as

��

�� (17)

where

��

��

��

� ��

�

��

��

�� (18)

and

��

��

� ��

�

��

��

��

��

(19)There is no loss of generality in assuming that � is uniformly

distributed on the interval �� for � � � � and � canbe expressed by � � �� Æ� where � � �� with �� and �� being integers such that� � �� , � � �� , �� and Æ� are realvalues in the range � � Æ� � ��. Substituting � into (18), (19)we found that

��

��

�

��

(20)where �� and �� are the consecutive data bits emitted bythe �th user, �� and � �

�� are defined by

�� Æ�

��

��

��

�� (21)

� �

�� Æ�

��

��

��

(22)

where �� and �� are the discrete aperiodic cross-correlation functions for sequences �� , �� and�� and ��, respectively, and �� is the sum of thefirst �� chips of sequence � ��.

The interference �� is modeled as a Gaussian processwith a probability distribution function of mean value � ��

and variance ��. Since ��, �� and ��,� �

�� are pairs of mutually independent random variablesand �� and �� are zero-mean independent random vari-ables with equal probable “1” and “-1” outcomes, the meanvalue �� is equal to zero. Consequently, the variance � �

��can be evaluated by

��

��

��

��

(23)

where �� is the expectation of the random variable � . Us-ing (21), (22) into (23) the variance � �

�� is given by

��

��

��

��

��

��

��

��

��

where �� is the discrete odd cross-correlation function forsequences � ��, � ��. For evaluating the BER we approx-imate �� by

��

��

��

��

The total MAI caused by �� transmitters at the receiver ofthe �th user can be modelled as the sum of � � independentrandomly distributed Gaussian processes, hence, the variance ofthe total MAI may be approximately calculated by

��

��

��

��

��

��

�� (24)

ACKNOWLEDGMENT

The authors would like to thank the anonymous reviewerswho gave valuable comments.

REFERENCES[1] T. O’Farrell and S. I. Lochmann, “Performance analysis of an optical cor-

relator receiver for SIK DS-CDMA communication systems,” Electron.Lett., vol. 30, pp. 63–65, 1994.

[2] L. Tancevsky et al.,“Incoherent asynchronous optical CDMA using Goldcodes,” Electron. Lett., vol. 30, pp. 721–723, 1994.

[3] F. Khaleghi and M. Kavehrad, “A new correlator receiver architecture forincoherent optical CDMA network with bipolar capacity,” IEEE Trans.Commun., vol. 44, no. 21, pp. 1335–1339, Oct. 1996.

[4] P. M. Lam, “Study of a novel hybrid optical-electronic code-divisionmultiple-access local area network based on Kronecker sequences,” Ph.D.dissertation, Asian Institute of Technology, Thailand, Dec. 1998.

[5] F. R. K. Chung, J. A. Salehi, and V. K. Wei, “Optical orthogonal codes:Design, analysis, and Applications,” IEEE Trans. Inform. Theory, vol. 35,pp. 595–604, May 1989.

[6] H. M. Shalaby, “Effect of thermal noise and APD noise on the perfor-mance of OPPM-CDMA receivers,” IEEE J. Lightwave Technol., vol. 18,pp. 905–914, July 2000.

[7] W. E. Stark and D.V. Sarwarte, “Kronecker sequences for spread-spectrumcommunication,” IEE Proc. Pt. F., vol. 128, no. 2, pp. 104–109, Apr. 1981.

[8] R. Gold, “Optimal binary sequences for spread spectrum multiplexing,”IEEE Trans. Inform. Theory, vol. IT-13, pp. 619–621, Oct. 1967.

[9] A. Lempel, M. Cohn, and W. L. Eastman, “A class of balanced binarysequences with optimal auto-correlation properties,” IEEE Trans. Inform.Theory, vol. IT-23, pp. 38–42, Jan. 1977.

[10] G. P. Agrawal, Fiber-Optic Communication Systems, 2nd ed., John Willey& Sons Inc., 1997.


Pham Manh Lam was born in Phutho, Vietnam,in 1956. He received the B.Eng degree in electro-mechanics from the Industrial Institute of Tournai,Belgium, in 1984 and the M.Eng and Dr.Eng. inTelecommunications from the Asian Institute of Tech-nology, Thailand, in 1992 and 1998, respectively.From 1985 to 1991, he was with the Institute ofInformation Technology, Hanoi, Vietnam, where heconducted research on data communication systems.Since 1999, he joined the Department of Telecommu-nication Science, Faculty of Science and Technology,

Assumption University, Bangkok, Thailand, where he is currently the directorof the Ph.D. program in Telecommunication Science. He is engaged in researchon optical code-division and time-division multiple-access techniques, codingtheory and digital communication systems. He is an oversea member of IEICEand a member of IEEE.

Do Quang Minh was born in HaNoi, Vietnam,in 1969. He received the B.Eng degree in radio-communications from the Moscow Institute of Com-munications, Russia, in 1992 and the M.Eng inTelecommunications from the Asian Institute of Tech-nology, Thailand, in 1997 and the M.Sc. in ComputerScience from Assumption University, Bangkok, Thai-land, in 2001. Since 1998, he joined the Departmentof Computer Science, Faculty of Science and Tech-nology, Assumption University, Bangkok, Thailand,where he is currently a lecturer in Computer Science.

He is engaged in research on coding theory, digital communication systems andcomputer graphics.

optical fiber code-division multiple-access networks using concatenated codes

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