optical code division multiple access network transmission...

Aminata A. Garba and Jan Bajcsy VOL. 3, NO. 5/MAY 2011/J. OPT. COMMUN. NETW. 435

Optical Code Division Multiple AccessNetwork Transmission With M-ary Chip

SymbolsAminata A. Garba and Jan Bajcsy

Abstract—This paper uses M-ary chip symbols to increasethe spectral efficiency of optical code division multipleaccess (OCDMA) even though, when compared to its binarycounterpart, M-ary OCDMA can have significantly increasedmulti-user interference (MUI). The presented numerical chan-nel capacity results show that appropriate non-uniform M-arysignaling allows the reduction of MUI and the achievement ofimproved OCDMA spectral efficiency. Using insights from theOCDMA capacity results, we design a coded M-ary OCDMAtransmission scheme that can achieve very high spectralefficiencies. The proposed time/wavelength OCDMA schemerelies on intensity modulation, appropriate non-uniformsignaling, M-ary trellis-coded modulation and error-correctingcodes. The corresponding receiver is based on direct detectionof optical signals, soft-decision single-user demodulation anderror-control decoding. The presented simulation results illus-trate that the designed OCDMA scheme can support hundredsof active users at the target bit error rate of 10−9 and is robustto impairments encountered in optical transmission (shotnoise, thermal noise). The achieved spectral efficiency of up to1.34 bits per OCDMA chip is significantly better than the bestbinary OCDMA result reported in the literature.

Index Terms—M-ary optical code division multiple access(OCDMA) transmission; Non-uniform signaling; Single-usersoft-decision demodulation and iterative decoding; Spectrallyefficient asynchronous OCDMA.

I. INTRODUCTION

O ptical code division multiple access (OCDMA) has beenwidely explored as a technology for military, government

and commercial optical networks, e.g., in [1–15]. OCDMAcan offer secure and flexible network transmission basedon the broadcast and select approach, direct sequencespreading and/or time/frequency hopping. Since users inOCDMA networks are non-orthogonal and asynchronous,severe multi-user interference (MUI) has been a key factorlimiting the performance of OCDMA transmission in boththeoretical and experimental studies. Although utilizing M-aryOCDMA instead of the traditional binary OCDMA would seemto be a natural approach to increase the achieved spectralefficiency, M-ary signaling by non-orthogonal users usually

Manuscript received October 27, 2010; revised January 28, 2011; acceptedFebruary 9, 2011; published April 28, 2011 (Doc. ID 137259).

The authors are with the Electrical and Computer Engineering Department,McGill University, 3480 University St., Montréal, Québec H3A 2A7, Canada(e-mail: [email protected]).

Digital Object Identifier 10.1364/JOCN.3.000435

leads to worse MUI than binary signaling. Consequently,binary OCDMA has been mostly studied in the literature sofar.

This paper presents results illustrating that M-ary OCDMAcan be used in such a way that it significantly outperformsbinary OCDMA. The comparison is done in terms of achievedspectral efficiency and ability to support many active OCDMAusers concurrently. We present relevant channel capacityresults and simulated bit error rate (BER) performance of acoded M-ary OCDMA system to show that the use of M-arychip symbols can increase data rates in OCDMA networkswhen compared to binary OCDMA systems. As in most priorliterature, we focus on OCDMA with single-user demodulationand decoding (SUD) due to practical implementation complex-ity constraints and signal processing speed requirements.

The structure of this paper is as follows. Section II includeschannel and noise models that describe MUI, the consideredoptical channel imperfections and channel noise. Consequently,Section III presents a channel capacity analysis for theconsidered M-ary optical CDMA transmission. In Section IV,we present the design of a coded OCDMA transmission schemethat is based on non-uniform M-ary channel input signaling,convolutional error-correcting codes (ECC), the designedtrellis-coded modulation and time/wavelength hopping. Thecorresponding receiver, described in the same section, usessoft-decision (single-user) demodulation and iterative (turbo)processing. Section V presents the simulation results for thedescribed M-ary OCDMA transmission corrupted by MUI,Poisson shot noise and additive white Gaussian noise (AWGN)thermal noise. Finally, Section VI concludes the paper.

II. CHANNEL MODELS

A. Overall Assumptions

We consider M-ary OCDMA network transmission withSUD at the receiver. K independent users (i.e., users who donot cooperate) send frame-asynchronous and chip-synchronousinformation data simultaneously over a fiber-optic channel,e.g., using a star coupler. (The chip-synchronous assumptionrepresents the worst case of chip-level interference.) Duringthe modulation, transmission and demodulation processes, theoptical signals are assumed to add up incoherently withoutbeatings and optical intensity direct detection is used at thereceiver.

1943-0620/11/050435-12/$15.00 © 2011 Optical Society of America

436 J. OPT. COMMUN. NETW./VOL. 3, NO. 5/MAY 2011 Aminata A. Garba and Jan Bajcsy

Fig. 1. Schematic block diagram of OCDMA network transmissionwith SUD at the receiver.

Under the above assumptions, we first describe a K-usercoded M-ary optical CDMA transmission at the chip levelwith appropriate discrete-time memoryless channel models, asillustrated in Fig. 1. The input of the multi-access channel isthe random variable X1 representing the symbol sent by user1, who is considered without any loss of generality. Channelinput X1 is consequently corrupted by interfering chip symbolsX2, X3, . . . , XK sent by other users and other sources of channelnoise. We assume that for all users, M-ary chip symbols xi =0,1,2, . . . , M−1 are sent with probabilities p0, p1, . . . ,pM−1.

We consider three types of OCDMA transmission:

1) idealized interference-only channel, when the transmittedsymbol X1 is corrupted only by MUI (X2 +·· ·+ XK );

2) low power OCDMA transmission when symbols arecorrupted by both the MUI and Poisson shot noise from theusers’ transmitters;

3) OCDMA channel with MUI and thermal noise from receiverelectronics.

The following three subsections describe these channels infurther detail.

B. Interference-Only OCDMA Channel Model

For the interference-only channel, the output of the OCDMAchannel is given by the random variable Y:

Y = X1 + X2 +·· ·+ XK , (1)

which can take values of 0,1, . . . ,K (M−1). Y represents thesum of the chip symbols sent by all K users of the networkat a given time instant. The entries of the resulting chip-levelchannel matrix PY |X1 are the conditional probabilities of theoutput symbol given the input symbol and can be described forall y ∈ {0,1,2, . . . ,K (M−1)} and x1 ∈ {0,1,2, . . . , M−1} by

PY |X1 (Y = y|X1 = x1)=∑

(x2 ,x3 ,...,xK )∈{0,1,2,...,M−1}K−1

s.t.x2+x3+···+xK=(y−x1)

px2 px3 . . . pxK ,

(2)

where px = P(X i = x).

C. OCDMA Channel With Optical Shot Noise

We consider the case when the dominant noise affectingOCDMA transmission is due to optical shot noise at theoptical transmitters, e.g., in the case of low power/low losstransmission. We will assume that µ is the average numberof photons used by each user to distinguish consecutive M-arylevels in chip transmission. Given that user i wants to transmitdata symbol xi ∈ {0,1,2, . . . , (M−1)}, the number of photons sentby his optical transmitter is conditionally Poisson distributedwith mean xiµ. Consequently, when users 1,2, . . . ,K sendsymbols x1, x2, . . . , xK , channel output Y, which represents thetotal number of photons received at the receiver countingdetector, is also conditionally Poisson distributed with a meanµ(x1 + x2 +·· ·+ xK )=µs, i.e.,

PY |X1,...,XK

(Y = y|X1 = x1, . . . , XK = xK

)= e−µs(µs)y

y!,

for all integers y = 0,1,2, . . .. In addition, the conditionalprobability mass function fully describing this single-userdecoded channel is given by

PY |X1 (Y = y|X1 = x1)=K(M−1)∑

s=0

e−µs(µs)y

y!

× ∑(x2 ,x3 ,...,xK )∈{0,1,2,...,M−1}K−1

s.t.x2+x3+···+xK=(s−x1)

px2 px3 . . . pxK , (3)

for all x1 = 0,1, . . . , M−1 and y= 0,1,2, . . ..

D. OCDMA Channel Model With Thermal Noise

In the case where the thermal noise from the receiverelectronics is the dominant external noise, the output of theOCDMA channel is given by

Y = X1 + X2 +·· ·+ XK +υ. (4)

In this case, channel input X1 is corrupted by MUI(X2 +·· ·+ XK

)as well as the Gaussian-distributed thermal

noise υ from the receiver electronics that is assumed to havezero mean and variance of σ2. Consequently, the conditionalprobability density describing this channel is given by

fY |X1 (y|x1)= 1p2πσ

M−1∑x2=0

M−1∑x3=0

· · ·M−1∑xK=0

e−1

2σ2

(y−

K∑i=1

xi

)2K∏

i=2pxi

,

(5)

for all real numbers y. In this case, we will define a normalizedchannel signal to noise ratio (SNR) per chip as SNR = 1/σ2, sothat it is independent of the channel input probabilities.


III. CHANNEL CAPACITY RESULTS AND INSIGHTS

A. Channel Capacity for OCDMA Transmission

We will use the symmetric sum capacity as an upper limit onthe aggregate data throughput achievable by the considered Ksymmetric OCDMA users during network transmission. Thiscapacity can be used as a benchmark when maximizing thespectral efficiency of a designed OCDMA system. When SUDis used, the sum capacity can be theoretically calculated bymaximizing the mutual information between the channel inputchip symbol X1 and the channel output Y over all channelinput probability mass functions PX1 :

C = K supPX1

I (X1;Y ) . (6)

The units of this capacity/spectral efficiency limit are normal-ized to bits per OCDMA chip. Note that for a specific channelinput probability mass function (PMF) PX1 , we also define theachievable throughput as K × I (X1;Y ) evaluated for PX1 . Theachievable throughput gives a spectral efficiency limit whenthe OCDMA transmitters use this particular channel inputPMF.

For the case of the interference-only OCDMA channelfrom Subsection II.B, we have numerically determined theexact sum capacity in [14] and it can be achieved usingan appropriate non-uniform channel input PMF. To simplifythe design of modulators/demodulators in Section IV, we willuse throughout this paper the following near-optimal channelinput PMF:

p0 = 1− 1K

and p1 = p2 = ·· · = pM−1 = 1K (M−1)

, (7)

which is close to the capacity-achieving optimal input PMFfrom [14]. Consequently, using the channel input probabilitymass function from Eq. (7), we calculate the achievablethroughput for

1) the interference-only OCDMA transmission described inSubsection II.B,

2) the shot noise dominated optical CDMA transmissiondiscussed in Subsection II.C, and

3) the OCDMA channel with AWGN-distributed thermal noisefrom Subsection II.D.

B. Throughout Results for Interference-Only OCDMA

It can be seen in Fig. 2 that, when all M-ary inputs are usedwith equal probability and the number of users K increases,the OCDMA spectral efficiency limit converges to 0.72 bits perOCDMA chip, even when the number of modulation levels Mincreases from M = 2 to M = 4,8,16. However, it is interestingto observe from Fig. 2 that the OCDMA network throughputcan be significantly enhanced by increasing the number ofmodulation levels and using non-uniform channel input PMFsgiven by Eq. (7).

Indeed, although increasing the number of modulationlevels is expected to increase the amount of MUI, the use

Proposed M-ary with M = 16




Equiprobable M = 2, 4, 8, 16

00

0.5

1

Thr

ough

put (

bits

/OC

DM

A c

hip)

1.5

2

2.5

50 100 150 200 250Number of users

300 350 400 450 500

Fig. 2. (Color online) Theoretically achievable rates for aninterference-only OCDMA network transmission with SUD.

Uniform input PMF

Non-equiprobable input PMF

00

50

100

150

200

250

Mul

tiuse

r in

terf

eren

ce

300

350

400

450

500

10 20 30 40 50Time instant (t)

60 70 80 90 100

Fig. 3. (Color online) Comparison of the amount of OCDMA MUI inthe cases of uniform and non-uniform channel input PMF from Eq.(7). The MUI is shown for different time instants t for K = 50 activeOCDMA users and M = 16 modulation levels.

of the non-uniform input PMF from Eq. (7) keeps the MUIreduced. Figure 3 illustrates the reduced MUI obtainedwith non-uniform channel input PMF and compares it tothe much larger amount of MUI resulting from uniformchannel input signaling. This reduction of the MUI throughnon-uniform signaling allows increase of the theoreticallyachievable spectral efficiency to almost 2 bits per chip forM = 16.

Moreover, as also illustrated in Fig. 2, the achievableaggregate throughput is steady for increasing number of activeusers and does not drop to zero. This is explained by thefact that the considered near-optimal input PMF from Eq. (7)depends on the number of active users and the probability ofthe MUI exceeding a given (often small number) is very low.Therefore, even if the total number of active users increases,the amount of MUI does not increase much.

Another key observation is that the MUI, when using thenon-uniform channel input PMF from Eq. (7), turns out to be


0.07

0.06

0.05

0.04

PMF

PMF

0.03

0.02

0.01

0 0

1

2

3

4

5

6× 10–3

0 50 500 1000 1500 2000100Interference level Interference level

150 200

(a) (b)

Fig. 4. (Color online) Histogram of MUI for 16-ary (M = 16)OCDMA transmission with K = 300 users. (a) Non-Gaussian MUIfor non-uniform signaling p0 = 0.9967; p1 = ·· · = p15 = 0.00022. (b)Gaussian interference with uniform PMF: p0 = p1 = ·· · = p15 = 1/16.

strongly reduced and non-Gaussian, as illustrated in Fig. 4 foran OCDMA network transmission, when 16-ary chip symbolsare used with the proposed probabilities from Eq. (7). On theother hand, many traditional approaches to OCDMA networktransmission with single-user decoding assume uniform chipsymbols, and the MUI converges in distribution to a Gaussianrandom variable due to the central limit theorem. In such acase, the transmitted data end up being severely corrupted bythe MUI, as also shown for illustration purposes in Fig. 4.

Consequently, since non-uniform channel input signalingleads to a reduced MUI and larger achievable transmissionrates, we will consider OCDMA transmission with non-uniformchannel input PMF for the rest of this paper.

C. Achievable Rates for OCDMA With Shot Noise

This section considers capacity limits on OCDMA transmis-sion affected by shot noise. Achievable rates for optical CDMAnetwork transmission corrupted by Poisson-distributed shotnoise are evaluated using the near-optimal channel input PMFfrom Eq. (7). Figures 5, 6 and 7 contain the main capacityresults that were obtained numerically and will be discussedin the following paragraphs.

In Fig. 5, the achievable transmission rates are shown forselected cases of M-ary modulation (M = 2,4,8,16) when µ =20 photons per M-ary modulation level are transmitted andnear-optimum channel input PMF from Eq. (7) is utilized.OCDMA network throughput of about 1.6 bits per chip istheoretically achievable in this case for M = 16 and a largenumber of active users. Although there is a capacity decreasedue to the shot noise (compared to the capacity for M = 16 andinterference only as illustrated in Fig. 2), a plateau is reachedfor M = 2,4,8,16 and increasing number of users. So eventhough the amount of shot noise increases with the number ofusers K, the OCDMA throughput does not drop asymptotically.

M = 16

M = 8

M = 4

M = 2

00

0.5

1

1.5

Thr

ough

put (

bits

/OC

DM

A c

hip)

2

2.5

50 100 150 200 250Number of users

300 350 400 450 500

Fig. 5. (Color online) Achievable throughput as a function of thenumber of users for selected M-ary OCDMA transmission with SUDat the receiver when the average number of transmitted photons isµ= 20 per M-ary level.

M = 16

M = 8

M = 4

M = 2

00

0.5

1

1.5

2

2.5

20 40

Thr

ough

put (

bits

/OC

DM

A c

hip)

60 80 100Number of photons per M-ary level

120 140 160 180 200

Fig. 6. (Color online) Achievable throughput as a function of µ, thenumber of transmitted photons per M-ary level, when the number ofusers is K = 500 for selected M-ary OCDMA transmission with SUD atthe receiver. (The horizontal dashed lines represent the limiting caseswithout shot noise for the considered M-ary OCDMA systems.)

Figure 6 illustrates the dependence of the throughput onthe average number of photons per OCDMA level (denotedµ), for a fixed number of active OCDMA users (K = 500)and binary, quaternary, 8-ary and 16-ary OCDMA symbols.One can observe in this figure that for small values of µ theachievable throughput is lower than the throughput achievablein the interference-only case, due to the effects of shot noise.Nonetheless, the performance of the interference-only OCDMAtransmission can eventually be reached by increasing theaverage number of photons per M-ary level. However, althoughusing µ = 20 photons per binary level may be sufficient to(almost) achieve the interference-only throughput with binaryOCDMA modulation, more than 80 photons per OCDMAlevel are required for 16-ary modulation to achieve a similarobjective. Hence, as the number of modulation levels increases,


Without Poisson noise

80 photons/ 16-ary level40 photons/ 16-ary level

20 photons/ level10 photons/ level

4 photons/ level

2 photons/ level1 photons/ level

2.5

2

1.5

Thr

ough

put (

bits

/OC

DM

A c

hip)

1

0.5

00 50 100 150 200 250

Number of users300 350 400 450 500

Fig. 7. (Color online) Achievable throughput limits on 16-ary OCDMAtransmission with SUD at the receiver for different numbers of usersK and numbers of photons per OCDMA level µ.

the average number of photons µ should be increasedaccordingly to allow better separation of user symbols fromthe shot noise effects. Finally, since the achievable throughputincreases in Fig. 6 with increasing number of modulation levelsM, one can conclude that OCDMA throughput gains due tonon-uniform M-ary signaling are robust to shot noise effects.

Figure 7 illustrates, in the specific case of M = 16 modulationlevels, the throughput limits for different numbers of activeusers and increasing average number of photons per OCDMAlevel. Not surprisingly, the aggregate throughput can beenhanced by increasing the average number of photons usedto separate different M-ary levels. However, even with averageseparation of one photon per 16-ary OCDMA level, theachievable throughput does not drop to zero, but reachesa plateau of about half the capacity without shot noise.This result is rather surprising, as only about a half of theinterference-only capacity would have been lost due to the shotnoise if a super-low power transmitter had been used. Finally,it can be observed that with about 80 photons per 16-aryOCDMA level, it is possible to approach the limiting capacityof the interference-only transmission.

Finally, Figs. 8 and 9 show the combined MUI and shot noiseaffecting OCDMA transmission in the cases of near-optimalnon-uniform chip signaling (a) and uniform chip signaling (b).One can observe the reduced and non-Gaussian nature of thechannel impairments affecting the transmitted symbols in thecase of near-optimal non-uniform signaling from Eq. (7).

D. Throughout Results for OCDMA With Gaussian Noise

This subsection explores the throughput limits for selectedM-ary OCDMA transmission with SUD in the presence ofthermal AWGN noise due to the receiver electronics. Weuse the near-optimum non-uniform signaling from Eq. (7)and numerically evaluate the channel throughput limits fordifferent values of M and signal to noise ratios.

0.4

0.35

0.3

0.25

PMF

PMF

0.2

0.15

0.1

0.05

0

0.025

0.02

0.015

0.01

0.005

00 20 40 60

Interference level80 100 0 20 40 60

Interference level80 100

0.45 0.03(a) (b)

Fig. 8. (Color online) Histogram of MUI and shot noise for 16-ary(M = 16) OCDMA transmission with K = 50 users and µ = 1. (a)Non-Gaussian MUI for near-optimal non-uniform channel input PMF:p0 = 0.98; p1 = ·· · = p15 = 0.013. (b) Gaussian interference withuniform PMF: p0 = p1 = ·· · = p15 = 1/16.

4

3.5

3

2.5

2

PMF

1.5

1

0.5

0

3

2.5

2

PMF

1.5

1

0.5

00 1000 2000

Interference level Interference level × 104

× 10–3 × 10–4

3000 1 2 3 4 5

(a) (b)

Fig. 9. (Color online) Histogram of MUI and shot noise for 16-ary(M = 16) CDMA transmission with K = 300 users and µ = 20. (a)Non-Gaussian MUI with non-uniform, near-optimal channel inputPMF: p0 = 0.9967; p1 = ·· · = p15 = 0.00022. (b) Gaussian interferencewith uniform PMF: p0 = p1 = ·· · = p15 = 1/16.

First, we observe how the OCDMA throughput limit changesat a fixed chip-level SNR. Figure 10 shows that for SNR =20 dB, the achievable spectral efficiency is close to theinterference-only case considered in Fig. 2 in Subsection III.B.This shows the robustness of the proposed OCDMA scheme toa practical amount of AWGN noise.

Figure 11 presents additional results that illustrate how thethroughput limit for M-ary OCDMA transmission increasesalmost linearly with increasing SNR until it reaches asaturation level. This saturation plateau occurs at around15 dB chip-level SNR for M = 2,4,8,16 modulation levels andis equal to the throughput limit of the same M-ary system inthe absence of noise (interference-only case). Consequently, as


M = 16

M = 8

M = 4

M = 2

5 100

0.5

1

1.5

Thr

ough

put (

bits

/OC

DM

A c

hip)

2

2.5

15 20 25 30Number of users

35 40 45 50

Fig. 10. (Color online) Achievable throughput against number of usersfor the selected M-ary OCDMA transmission with SUD at the receiverat 20 dB chip SNR.

M = 16

M = 8

M = 4

M = 2

0

0.5

1

1.5

2

2.5

5 10 15SNR (dB)

Thr

ough

put (

bits

/OC

DM

A c

hip)

20 25 30

Fig. 11. (Color online) Achievable throughput as a function of chipSNR for the selected 50-user M-ary CDMA transmission with SUD atthe receiver.

the SNR increases, the spectral efficiency can be significantlyimproved with M-ary modulation using the non-uniformchannel input PMF from Eq. (7), when compared to both binaryand uniform M-ary OCDMA transmission.

IV. PROPOSED OCDMA TRANSMISSION SCHEME

Our aim is to design a scheme for OCDMA networktransmission and reception that exploits the capacity gainsof OCDMA with non-uniform M-ary chips from Section III.We extend our recently proposed wavelength–time OCDMA-spreading approach [15] from binary to the case of M-arymodulated symbols and also incorporate an additional M-ary trellis-coded modulator (TCM) as well as an iterativereceiver that uses turbo-demodulation. In addition, we alsodescribe three single-user OCDMA demodulators that allow

soft-decision demodulation of a signal corrupted by MUI andshot (or thermal) noise.

A. Proposed Transmission Scheme

Figure 12 shows the overall schematic block diagram of theconsidered optical CDMA network transmission scheme with Kusers transmitting data simultaneously, frame asynchronouslyand independently of each other. Each user’s data packet isfirst encoded using a Reed–Solomon code, then interleavedand encoded by a convolutional code. Consequently, theencoded data are modulated using a TCM which maps theencoded binary packet into an M-ary data stream composedof equiprobable symbols 0,1,2, . . . , M−1.

Each TCM encoded packet is consequently sent through auser-specific OCDMA modulator that uses wavelengths λ =1,2,3, . . . ,Λ and time slots t = 1,2,3, . . . for data transmission.As shown in detail in Fig. 13, the modulator first arrangeserror-control coded bits of a given user into consecutivetwo-dimensional arrays of size Λ by T. Consequently, it padseach array with Z columns, all containing zero symbols, where

Z = T × K (M−1)−MM

. (8)

These deterministic zero symbols, which we will call zero-padded symbols, are inserted into the stream of modulatedM-ary chip symbols in order to achieve near capacity-achievingchannel input probability from Eq. (7). Afterward, a user-specific channel time-interleaver pseudo-randomly permutesthe columns of each 2-dimensional data array to distributedata and padded symbols evenly in the transmitted packets.Finally, the user’s data are optically modulated by the E/Omodule shown in Fig. 12. The optical intensity signal xi(t,λ),sent at time t and wavelength λ, corresponds to the appropriateentry of the 2-dimensional data arrays sent by user i.

As a result of this OCDMA modulation approach, thechannel use probability by each active user is

Pch = MK (M−1)

. (9)

Note that Pch corresponds to the fraction of the time whena user sends error-control coded chip symbols directly over thechannel, as opposed to sending the zero-padded symbols.

B. Proposed Receiver

As illustrated in Fig. 12, the proposed single-user receiveris composed of an appropriate optical to electrical signalconverter (O/E), a soft-decision OCDMA demodulator and aniterative decoder that is followed by a Reed–Solomon decoder,all separated by appropriate interleaving/de-interleaving.The O/E module of the OCDMA receiver first performsintensity detection for each separate time–wavelength slot,thus generating electrical signals proportional to the receivedsignal y (t,λ) at each time instant t and for each wavelengthslot λ. Consequently, at each time instant t for which the usersent a coded data symbol over the channel (i.e., not a padded


Fig. 12. (Color online) Schematic block diagram of the proposed OCDMA transmission scheme with SUD at the receiver. (Electro-optic andopto-electric signal conversion is performed by the E/O and O/E modules and data interleaving/de-interleaving is performed by modules denotedby pi i ,πi ,Πi ,π

−1i ,Π−1

i , pi−1i ).

-

Fig. 13. Detailed operation of the proposed M-ary wavelength–time OCDMA modulator: twelve symbols that were error-control encoded and16-ary TCM encoded are rearranged into a time/wavelength array with parameters T = 3 and Λ = 4, padded with Z = 5 all-zero columns andtime-interleaved prior to being sent through the optical channel.

0 symbol), we use an appropriate chip-level soft-decisionOCDMA demodulator defined in the next subsection. Thedemodulator generates a posteriori probability estimates aboutthe M-ary TCM coded symbols of the desired user whichare then fed into a soft-decision TCM decoder and an error-correcting convolutional decoder. The TCM and convolutionaldecoders are connected in an iterative decoding loop inwhich they exchange extrinsic information estimates about theerror-control coded bits by applying the turbo-demodulationapproach from [16]. After a prescribed number of iterations,the convolutional decoder passes its hard decisions to theReed–Solomon decoder that estimates the message bits of thedesired user.

C. Soft-Decision Demodulators

We describe the design of several M-ary OCDMA demodula-tors to be used in the architecture of Fig. 12 in the presenceof various channel impairments. The OCDMA single-userdemodulators use the appropriate channel model from Eq.(3) or Eq. (5) and the Bayes’ rule to generate a posterioriprobability estimates about the coded M-ary chip symbols ofa given user.

These a posteriori probabilities about the coded bits ofdesired user 1 are given for the OCDMA channel with Poisson

shot noise as

PX1|Y (x1 (t,λ)= m|y (t,λ))=αK t(M−1)∑

j=0

e−µ j(µ j)y(t,λ)

y (t,λ)!P j|m

(10)

and for OCDMA transmission with AWGN thermal noise as

PX1|Y (x1 (t,λ)= m|y(t,λ))

=α(K t−1)(M−1)∑

j=0e

−12σ2 (y(t,λ)−(m+ j))2

P j|m. (11)

Note that in the two previous equations, α denotes a normal-ization constant and K t is the number of users transmittingdata (not zero-padded symbols) at time t (Appendix A describesa way in which K t can be determined in practice.) Finally, P j|mrepresents the conditional probability that the sum X1 + X2 +·· ·+XK is equal to j when the channel input X1 = m, i.e., P j|m =Pr(X1 + X2 + ·· · + XK = j|X1 = m). This quantity can beevaluated for all j = 0,1,2, . . . ,K (M−1) and m = 0,1,2, . . . , M−1as follows:

P j|m = ∑(x2 ,x3 ,...,xK )∈{0,1,2,...,M−1}K−1

s.t.x2+x3+···+xK=(y−x1)

px2 px3 . . . pxK . (12)


V. SIMULATION RESULTS

This section presents BER performance results for theM-ary OCDMA transmission scheme from Fig. 12 in thepresence of MUI and noise (shot or AWGN). The OCDMAtarget BER is 10−9 and the simulated results presented in thissection show that the considered M-ary OCDMA architecturefrom Fig. 12 can achieve high spectral efficiencies of up to 1.34bits per OCDMA chip.

A. System Parameters

We considered a 16-ary (M = 16) OCDMA networktransmission system with SUD at the receiver. We employeda (255, 239) Reed–Solomon code over a Galois field (GF)(256) [17] followed by the rate 1/2 convolutional encoder withthe generator polynomials of the constituent encoders beingg1(D)= 1⊕D3 ⊕D4 and g2(D)= 1⊕D⊕D3 ⊕D4.

Figure 14 shows the trellis diagram of a 16-ary non-recursive TCM encoder with 16 states and rate two that wasdesigned using Ungerboeck’s set-partitioning rules [18]. Thetwo binary input symbols and the corresponding 16-ary outputsymbol are illustrated for the four transitions ending at eachstate.

The time/wavelength OCDMA modulators used Λ = 62wavelengths for data transmission and channel access proba-bility Pch = 0.0032. The system also used a 63rd wavelength todetermine K t, the number of actively interfering users at eachtime instant t, and a 64th wavelength for other protocols, asdiscussed in Appendix A. User-specific pseudo-random channel

interleavers are utilized to permute M-ary TCM symbols on thechip level. We also used pseudo-random interleavers of length10,000 between the error-correcting encoder (Reed–Solomonand convolutional encoder) and the TCM encoder.

The soft-decision TCM and convolutional decoders, con-nected in an iterative decoding loop shown in Fig. 12, used theBCJR algorithm [19]. The Reed–Solomon decoder is appliedafter a prescribed number of decoding iterations to lower theend-to-end BER below the target value of 10−9.

The achieved spectral efficiency at the target BER of 10−9

is determined for the proposed architecture in Fig. 12 as theaggregate rate of the coding and modulation schemes for allthe K users of the network as follows:

η= KNumber of users

× RcECC Code rate

× RmodRate of the OCDMA modulator

bits/ OCDMA chip, (13)

where K is the total number of active OCDMA users thatcan be supported on the network at BER = 10−9, Rc is thecombined rate of the convolutional, TCM and Reed–Solomoncodes (respectively RCC , RTCM , RRS). Finally, Rmod is therate of the zero-padding OCDMA modulator which can becalculated as Rmod = Pch × 62

64 , where Pch is the probability ofchannel use defined in Eq. (9) defining the ratio of the numberof actual data symbols over the number of combined dataand zero-padded symbols. The number 62/64 above representsthe ratio of the number of wavelengths used for actual datatransmission over the total number of wavelengths (since twowavelengths have been dedicated to determine K t and othernetwork considerations).

0010

0011

0100

0101

0110

0111

1001

1010

1011

0001

1100

1101

1110

0000

1111

1000

0010

0011

0100

0101

0110

0111

1001

1010

1011

0001

1100

1101

1110

0000

1111

1000

00 / 0,10, 8, 2

00 / 2, 8, 10, 0

00 / 6, 12, 14, 4

00 / 4, 14, 12, 6

10 / 11, 1, 3, 9

10 / 9, 3, 1, 11

10 / 13, 7, 5 ,15

10 / 15, 5, 7, 13

01 / 2, 8, 10, 0

01 / 0, 10, 8, 2

01 / 4, 14, 12, 6

01 / 6, 12, 14, 4

11 / 11, 1, 3, 9

11 / 9, 3, 1, 11

11 / 15, 5, 7, 13

11 / 13, 7, 5, 15

Fig. 14. (Color online) One stage of the designed trellis diagram for the rate two, 16-ary TCM encoder. (Note: all trellis edges entering a givenstate have the same input labels.)


Consequently, the spectral efficiency can be written as

η= K × (RCC ×RTCM ×RRS

)×(Pch × 62

64

)bits/OCDMA chip.

(14)

B. BER Performance Results

We first considered an OCDMA transmission where thePoisson shot noise is the dominant noise. Initially, theconsidered number of photons per 16-ary modulation level islimited to µ = 20 and Fig. 15 illustrates the obtained BERperformance. It can be seen that up to K = 298 active users canbe supported at the target BER= 10−9 after seven iterations ofthe iterative decoder followed by Reed–Solomon decoding. Thiscorresponds to an achieved spectral efficiency of

η= 298×(

12×2× 239

255

)× 62

64×Pch = 0.86 bits/OCDMA chip.

After increasing the average number of photons to µ = 40photons per 16-ary level, Fig. 16 presents the simulated BERperformance results. The number of supported users on theOCDMA network is K = 368 active users, after 10 decodingiterations and Reed–Solomon decoding. This corresponds to anachieved spectral efficiency of

η= 368×(

12×2× 239

255

)× 62

64×Pch = 1.07 bits/ OCDMA chip.

When the average number of photons is increased to µ =80 photons per 16-ary level, the performance results for anOCDMA transmission with Poisson shot noise are shownin Fig. 17. The achieved spectral efficiency at BER = 10−9

improves to

η= 418×(

12×2× 239

255

)×Pch × 62

64= 1.21 bits/OCDMA chip.

1 iteration2 iterations3 iterations4 iterations7 iterations

2 iterations3 iterations4 iterations7 iterations

24010–4

10–3

10–2

10–1

100

250

BE

R

10–12

10–10

10–8

10–6

10–4

10–2

100

BE

R

260 270 280Number of users

290 300 310 240 250 260 270 280Number of users

290 300 310

(a) (b)

1 iteration

Fig. 15. (Color online) BER performance of the designed 16-ary OCDMA transmission corrupted by Poisson shot noise, when the number ofphotons per 16-ary level is µ= 20: (a) after convolutional decoding and (b) after both convolutional and Reed–Solomon decoding.

1 iteration2 iterations3 iterations4 iterations7 iterations10 iterations


30010–4

10–3

10–2

10–1

100

310

BE

R

10–12

10–10

10–8

10–6

10–4

10–2

100

BE

R


350 360 370 380 390 300 310 320 330 340Number of users

350 360 370 380

(a) (b)

Fig. 16. (Color online) BER performance for the designed 16-ary OCDMA transmission scheme with non-uniform signaling in the presenceof Poisson shot noise. The number of photons per 16-ary level is µ = 40 and the BER is shown after (a) convolutional decoding and (b) bothconvolutional and Reed–Solomon decoding.




35010–4

10–3

10–2

10–1

100

360

BE

R

10–12

10–10

10–8

10–6

10–4

10–2

100

BE

R


400 410 420 430 440 450 460 350 360 370 380 390Number of users

400 410 420 430

(a) (b)

Fig. 17. (Color online) BER results of the designed 16-ary OCDMA transmission scheme with non-uniform signaling when shot noise with µ= 80photons per 16-ary level corrupts the transmission after (a) convolutional decoding and (b) both convolutional and Reed–Solomon decoding.

Moreover, we also considered the OCDMA network trans-mission with thermal noise from the receiver electronics,modeled by an AWGN noise. (The normalized chip-levelchannel SNR is defined as 1/σ2 = 20 dB.) The simulationresults in Fig. 18 demonstrate that the proposed OCDMAscheme can support an even larger number of active users.Indeed, after 12 decoding iterations, up to K = 462 active userscan be supported at the target BER = 10−9. The achievedspectral efficiency is

η= 462×(

12×2× 239

255

)× 62

64×Pch = 1.34 bits/OCDMA chip.

C. Observations and Discussion

Overall, the designed coded M-ary OCDMA system fromFig. 12 performs well in all cases considered in Subsec-tion V.B. We observed that a significant BER performanceimprovement occurs as the iterative receiver iterates andeliminates the effects of MUI and channel noise from the

soft decisions provided by the OCDMA demodulator. Theachieved spectral efficiency and BER performance resultsshow that the proposed M-ary OCDMA transmission schemeis robust to several impairments encountered in OCDMAtransmission, i.e., MUI, Poisson-distributed shot noise andGaussian-distributed thermal noise.

In addition, we also observe that as the average numberof photons per symbol level increases, the performance ofthe proposed M-ary OCDMA system with Poisson shot noiseimproves. Hence, in the limiting case of high average numberof transmitted photons, the system performance is not muchlimited by the Poisson noise, but the MUI becomes the mainsource of errors.

It is interesting to note that the considered non-uniform M-ary OCDMA transmission scheme achieved a spectral effi-ciency of 1.34 bits per chip, which is significantly betterthan what the best uniform M-ary OCDMA system canachieve (0.72 bits per chip based on the capacity analysisresults in Section III). Furthermore, the spectral efficiency of1.34 bits per chip, achieved by the considered non-uniformM-ary OCDMA transmission with AWGN thermal noise, is



10–4

10–3

10–2

10–1

100

BE

R

BE

R

10–7

10–6

10–5

10–4

10–3

10–2

10–1

100

380 390Number of users

400 410 420 430 440 450 460 470 480 380 390Number of users

400 410 420 430 440 450 460 470 480

(a) (b)

Fig. 18. (Color online) BER of the proposed 16-ary OCDMA transmission system with AWGN thermal noise and non-uniform input signalingafter (a) iterative decoding and (b) iterative decoding followed by RS decoding.


- almost twice the spectral efficiency of 0.74 bits/chipachieved by the best previous binary OCDMA system [15];

- more than three times better than the 0.36 bits/chipachieved by the M-ary OCDMA system reported in [14].

Finally, it is interesting to observe that the key reasonbehind the achieved high OCDMA spectral efficiency is thereduction of the number of actively interfering users K t. Toillustrate this point in further detail, Fig. 19(a) shows thenumber of actively interfering users K t on the channel forK = 300 active OCDMA network users and channel accessprobability Pch = 0.0032. It can be seen that although thetotal number of active network users K = 300 is high, K t israther small. This observation is also illustrated in Fig. 19(b)through the probability distribution of K t for a large numberof active users K. Therefore the single-user receiver has todeal with significantly reduced MUI due to the transmitters’actions (i.e., appropriate non-uniform M-ary signaling). ThisMUI reduction in turn allows benefit to be gained from the rateincrease due to M-ary signaling, when compared to binary oruniform M-ary OCDMA.

VI. CONCLUSION

This paper presented capacity results and insights forM-ary OCDMA network transmission in the presence of MUI,Poisson shot noise and AWGN thermal noise. It was observedthat the use of appropriate non-uniform M-ary signalingleads to reduction of the MUI and high achievable spectralefficiencies. Using the insights from the capacity results, wepresented the design of a time/wavelength M-ary OCDMAnetwork transmission scheme that relies on single-userdemodulation/decoding and error-control coding.

The simulated BER performance results illustrated that thedesigned M-ary OCDMA scheme allows the achievement ofhigh spectral efficiencies of up to 1.34 bits per OCDMA chipand can support large numbers of active users. Furthermore,the proposed scheme is robust against several impairmentswhich occur in OCDMA network transmission such as MUI,Poisson shot noise and AWGN thermal noise. Finally, insights

were presented which explain the improved performanceachieved by the designed M-ary OCDMA system.

APPENDIX A

This appendix discusses how the OCDMA network receiversfrom Fig. 12 can tune into the transmission of a particulartransmitting user when dealing with network broadcastingand/or multicasting. The appendix also describes how thereceiver can determine the value of K t that is used forsoft-decision demodulation in Section IV. Finally, it alsopresents the probability distribution of the reduced MUI forthe proposed OCDMA transmission that uses non-uniformM-ary signaling.

Appendix A.1 Networking Considerations

One way to achieve the objectives described in the previousparagraph is by dedicating two additional wavelengths forOCDMA network protocol implementation.

The wavelength (Λ+ 1) would be used to determine K t,the number of actively interfering users who transmitted data(not zero-padded symbols) at time instant t. In particular,when at time t a user transmits T coded symbols over Λwavelengths of the optical channel he/she also sends a unitintensity signal at the dedicated wavelength (Λ+1). (Note thatthe user sends a zero intensity signal at this wavelength whensending padded zero-padded symbols at time t.) As a result,the combined optical signal intensity at wavelength (Λ+ 1)at time t is proportional to K t, the number of users sendingnon-zero-padded symbols at this time instant.

The wavelength (Λ+2) can be used to allow frame synchro-nization and tuning into transmission of a particular user by areceiver or receivers in the case of broadcasting/multicasting.In particular, each user uses a user-specific optical time-spreading sequence to distinguish his/her transmitter fromother transmitters. When the user is actively sending data overthe network using wavelengths λ= 1,2,3, . . . ,Λ, his/her opticaltime-spreading sequence is also transmitted periodically at

4

3.5

3

2.5

Num

ber

of in

terf

erin

g us

ers

PMF

2

1.5

1

0.5

0

0.4

0.35

0.3

0.25

0.2

0.15

0.1

0.05

00 10 20 30 40 50

Time instant (t) Interference level60 70 80 90 100 0 1 2 3 4 5 6 7 8 9

(a) (b)

Fig. 19. (Color online) The number of actively interfering users K t when the total number of users is K = 300 for the proposed OCDMA scheme,when M = 16 and the channel access probability is Pch = 0.0032: (a) K t is shown at different time instants t; (b) histogram of K t.


wavelength (Λ+2). Although this optical-spreading sequenceis not used for actual data transmission at wavelength (Λ+2),a receiver or receivers can use a traditional OCDMA matchedfilter to scan the wavelength (Λ+ 2) for the presence of thedesired user. Occurrence of the autocorrelation peak in thematched filter output indicates that the desired user is activeand the peak’s timing can be used to adjust/synchronize thereceiver to the frame timing of the particular transmitter.Finally, the pseudo-random interleavers, used by the OCDMAtransmitters in Fig. 12, can be fixed for each user and specifiedby seed in a common pseudo-random number generator, so thatall receivers know the interleavers parameters.

Appendix A.2 Reduced Multi-user Interference

It is also interesting to observe that the proposed OCDMAtransmission approach reduces the amount of MUI even whena large number of active users K is transmitting data over theOCDMA network. Indeed, the probability mass function of thenumber of actively interfering users K t is given, for 0≤ j ≤ K−1,by

P (K t = j)=(K −1

j

)(1−Pch

)K−1− j(Pch) j . (15)

For a large number of users, the above probability reducesto

P (K t = j)−→ 1j!

(M

M−1

) je−

MM−1 ,

which corresponds to a Poisson distribution with parameterM/ (M−1). Note that P(K t = j) is quickly decreasing forj ≥ 1, as illustrated in Fig. 19. Consequently, the number ofinterfering users K t is usually low at each time instant t, evenwhen the total number of active network users K is very large.As an example, for the M = 16 modulation level and K = 500active users on the network, the probability of having five orless actively interfering users is 0.9971.

ACKNOWLEDGMENTS

This work was supported in part by the National Science andEngineering Research Council (Canada) and the CanadianFoundation for Innovation. This work has been presented, inpart, at IEEE Globecom 2007.

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