Performances of LDPC based multi-user space time diversity system design for uplink multi-carrier CDMA

MJ. Syed, G. Ferre, J.P. Cances, V.Meghdadi, G.R.M. Khanif University of Limoges, ENSIL-GESTE

Pare ESTER B.P 6804, 87068 LIMOGES CEOEX, France {syed, ferre, cances, meghdadi }@ensi1.unilim.fr

Abstract-We examine the performanees of a multiuser spaee time diversity system for uplink environment when it is interface!!. by a LOpe code. The proposed structure uses a new combination ofSTBC, OFDM and CDMA spreading. The OFOM codewords are built from chips issued from different symbols. The STBC encoding is done at the last stage of the transmitter and we place STBC decoder after multiuser mitigation. We show that our system is particularly easy to implement while obtaining similar performance compared to a single user STBC system. We show furthermore that the performance of the system when concatenated with LOPC code can be increased when an additional large symbol interleaver is used.

Keywords - STBC. uplink multi-user detection. multi-carrier. CDMA, LDPC. MfMO channel

I. INTRODUCTION Space-time coding (STC) techniques, including space-time

trellis coding (STTC) and space-time block coding (STBC) integrate the techniques of antenna array spatial diversity and channel coding providing significant capacity gain in wireless channels. Several papers have investigated their use particularly for the case of wireless flat-fading channels (I]. However, many wireless channels are frequency-selective in nature, for which the STC design problem becomes a complicated issue. On the other hand, the orthogonal frequency-division multiplexing (OFOM) technique transforms a frequency-selective fading channel into parallel correlated flat-fading channels. Stamoulis et a1. have shown

niques. Vook et a1. extended this idea with antenna diversity in [8]. Other STBC - COMA based system with MMSE filtering techniques have been proposed by Auffray et a1. [9].

We propose here an uplink COMA based multi-user system with space diversity over frequency selective channels. OFOM technique is used to combat the frequency selective channel. Our proposed system can be viewed as an extension of Multi­Carrier Direct Sequence CDMA (MC-OS-COMA) techniques with antenna diversity and OF OM cycl ic prefixing. The proposed system is the direct adaptation of (10] to space time block codes which could achieve higher rate than [6]-[8J. We show that our design is particularly easy to implement, and besides, the performance is cQmparable to the case of a single user STBC system. The overall system can be decoupled into K single carrier COMA system with antenna diversity. This makes the system highly parallelizable. Furthermore, all techniques known for single carrier COMA or STBC systems can be therefore adapted to our system provided that the

r Laboratoire des signaux et systemes (L2S),SupeJec 3 rue Joliot-Curie, 91190 Gif-sur-Yvette (France)

gholam-reza.mohammad-khani@lss.supelec.fr

that a multiple user STBC system under a flat fading environment is feasible with a simple linear processing technique as long as the receiver has at least the same number of antennas as the number of users (2]. Naguib proposed a multi-user STBC system in a multi-path channel environment using a frequency domain equalizer (FDE) (3]. He has shown that in frequency domain, the detection can be made individually to each sub carrier. Adaptation of this proposal to OFDM system is straightforward. The drawback of this system is that the number of required receive antennas is proportional to the number of users. The increase of the number of antennas to cope with more users is without any space diversity gain. So it is natural to consider another multiple access technique such as Code Division Multiple Access (COMA). Liu et al. have proposed a generalized complex STBC design with precoders particularly well suited for Multi-CaTTier-COMA (MC-CDMA) downlink environment [4J. Stamoulis et al. extended this idea to uplink environment in [6]. While the three level approach in [4] and [6] made the system flexible, the main drawback is that a set of different subcarriers is allocated to each user. An STC multi-carrier COMA system has been proposed by Yang et al. with different spreading signature for each transmitter antenna [5]. Baum et al. proposed cyclic prefixed single carrier CDMA for downlink application in [7] to make use of the efficient FOE and MMSE tech

channel stays invariant during a STBC word. As we state in [10], the performance of our multiuser space time system can be increased when an additional large symbol interleaver is used. In this paper, we first present OUT transmitter and receiver architecture and then present computer simulation results to illustrate the performance of our system.

II. SYSTEM DESCRIPTION

A) Overview The simplified transmitter model for one user is represented

in Fig I. The system functions in blocks of PxK symbols. K denotes the number of tones in OFOM subsystem and P denotes the number of symbol necessary to build an STBC

codeword. The PxK symbols are rearranged to form P vectors of K symbols using the serial to parallel converter (SIP). On each branch of SIP output, the P symbols are spreaded using a code of length e.

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Fig 1 : Transmitter Model

The PxK EI-sized vectors are then rearranged to form P K>;'8matrices. IDFT is then applied to each column of each matrix, to form pxO OFOM code

·words.We note X(Jp the ph

e-!=o�ewords and {X } represent an STBC qp pE{o .. . . P-11

codeword. q p will be used to invariantly represent the pth

symbol constituting a STBC codeword. These P matrices will be then dispatched into N STBC antennas and will be sent over P' matrices timeslot. PIP' define the rate of the STBC subsystem. Our STBC construction differs slightly from the symbol based STBC system proposed in [11]-[12] or from the vector based STBC system in [3]. We send N matrices at each STBC timeslot, and the matrices are specially formed so that the symbols obtained after MultiUser Interference (MUI) elimination are orthogonal. For the sake of clarity, we will limit our scope in this paper to a two-transmit-antenna system, as the generalization to N transmit antennas is straightforward.

To make multiple user access possible, we need to design and distribute the spreading codes to all users while maintaining the orthogonality between users. In a simple case, each user will be atlribut�d one spreading code to be used over all sub carriers.

Let {C1 . . . . ,ce } e'ifthe set of all possible combinations of

real valued orthogonal spreading sequence with

cli =[cu (I) , .... cu (9)] r . The set 'f' will permit us to have at Oxl

most e users in the system. Each user symbol is actually being sent over one sub carrier only, and the spreading signature is applied to each symbol over each sub carrier. For simplicity, in this paper, we will first use orthogonal codes such as Walsh Code.

Let C=[C1 .. . ce] T the matrix of all available spreading 0xO

code. If we attribute to each user u, a unitary permutation matrix Pu condition that

T VIl. TJ: PI-' . Pll = b� . I (I) we can define e", the user code as

(2)

and we have

VIl,TJ:P� .p/ =b�·[1JK'K' 8� denotes the Kronecker delta.

The code allocating scheme presented in [10] can be used too.

B) Transmitter model Let bu = {bu.q, ,bu,q, } the 2xK symbols to be s�nt by 'user u

with bu.qp =[bu.t}p (I) .. . bu,qp (K)] . The spreading operation

can be modeled by a matrix multiplication

(3)·

with Bu,qp =diag(bu,tjp t'K' Each line in su.qp represents the

sequence to be sent over the respective sub carrier 'and each column indicates the time as shown in Fig. 2. We create OFDM codewords from each column of (3) represented by simple matrix multiplication between the 10FT matrix and sU.(Jp • We have

X =Q'.s (4) U,tjp u.qp Q is a KxK OFT matrix with Qm.n

= (J/.J"K)e-J2rrmn/K .

Fig. 2 : Spreaded sequences over sub carrier

These OFOM codewords will be rearranged to produce our special STBC system. In our two transmit antennas

configuration, we will send successively 1 Xu,q, • XU,q,} over

the first antenna and {-Xu.q, ,XU,q,} over the second antenna,

with X =J·X' (5) r.(,'1/J u.ljp

and J the skew eye matrix representing the OFOM codeword

ti� ,,,,,,,I, J=[� . . ' :l A, ,ho� In Fig 3, nolo tho! th,

OFOM codeword time reversal is not the same as spread sequence time reversal as the OFDM codeword time reversal is done immediately after the parallel/serial converter in the OFOM modulator. Table 1 and Fig. 4 resumes the transmit operation.

Fig 3 ; Time reversed OFDM codewords

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. l!!lZ!!Iirf r x.._111� . lliJ Ui ·[llH�I!I!ZiIll·! �<O,Glj : ' ..

� j.i1.44iCI>J[rnlJml'�� l;�

Fig. 4 : Data transmission over time and antenna (ep denoles cyclic prefix) Each OFDM codeword is sufficiently prefixed to ensure that

there will be no inter block interference (fBI) between two OFDM codewords. The prefix length will depend on the frequency selective channel.

TABLE 1 : TRANSMJTOPERATION OVER SPACEANDTJME

C) Receiver model The receiver structure is represented in Fig. 5. In an uplink

configuration, each user will have its own frequency selective channel between each transmit and receive antenna pair. Considering the channel response of ulh user between its /h transmit antenna and 1<11 receiver antenna, the channel is modeled as L-I (1 )

hi.;(t)"" 2>�.i (lP t--I�O !if

(6)

with L=[trn�f + I], tm is the maximum delay in any user

frequency selective channel, a],; (l) is the f' complex value

tap gain, and !if the whole bandwidth of the OFDM system. All user signals emitted from all transmit antennas,

propagate through their respective frequency selective channel and reach the lh receiver antenna. These superposed signals are affected with an additive complex White Gaussian noise

(A WGN) with variance cr� per dimension. It is assumed that channels are not correlated, and are invariant during our STBC codeword.

L

Fig. 5 : Receiver Model Denote Nu the number of user in the system. Considering a

quasi synchronous system as in a micro cell environment, the received signal for each OFDM codeword can be represented as

N.

Y;,q, (K)= L>'�; 0 Xu ,'I, (K)-h�.1 ® Xu,q, (K)+ N'II (K) (7) u=.

N.

Y;"I, (K)= �>'�j0Xu,q, (K)+h�.I0Xu.'11 (K)+N", (K) (8) u=)

where XU"}p (K) represents the J<th OFDM codeword from the

matrix Xu.g, (or the J<tlt column from the same matrix) and

o denotes the convolution operator. Following [3], the above equations can be written in matrix form as

N.

Yj.'I, (K)= L"�,' ,X. 'II (K)-"�.i·X.'I" (K)+Nq, (K) (9) N.

Yl.q, (K)= LH�,i'Xu"" (K)+H�.i'X",(J, (K)+Nq, (K) (10) u=l

With a proper cyclic extensions and sample timing, and tolerable leakage, "j,; is a KxK circulant matrix, and can be

eigenvalue decomposed as

H".. =Q* ·Au .. Q (II) j.I j,J

with AU. = diag (Q. aU . ) and a"·· is the same as (6) with j,1 J ,1 }.1

a�J = [ a�.i (0) . . . ajAL-I)Y-. Supposing invariant channel during a STBC codeword, and

knowing that

Q'x' (n)=DFT(x' (n))=DFT(X( -n))' =DFT(J . X (n))" from the Fourier transform duality and (4), (9).( 11), we obtain

N,

Y;.q, = LQ' ·Al.! '5.,'11 -Q' .A?>s�,q, +Nq, (12) .=1

(13)

with Yi.qp = [Yi,qp (I) ... Yi,qp (K) .. . Y;,C}p (e)t'9 After DFT operation related to OFDM modulation, we have

r"qp =Q·Yi.qp , and

N,

fi.q, = LAl.i·S".'11 - AL · s: .q, +0'1, (14) Ii"") N"

r· = � AU1··s +Au . ,s· +0 r,ff'!, L.. .1 u,q:1. 2.1 I-i.t]\ lJ';1 (\5) u:::;1

At this stage, each line in the riq I matrix represents the • P KxB

superposition of all spreaded user symbols sent over a distinct sub carrier during a STBC codeword. Due to OUT code repartition system, and analog to a single carrier CDMA system, we can retrieve any user symbol by multiplying the received noisy vector by the corresponding user code. We can therefore discriminate all user symbols by multiplying vectors received at each sub carrier by C. Hence, if Zi.qp =rj,qp ·CT , we have

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u=1

N. Z = '" AUI··s ·CT +A"2' '5' 'CT +Oq ·CT J.q� � ,I u.q� ,r U.ql :;

.=1 N, '" U • U " T '" L.,.;AJ.j.Bu,q, ·Pu+AV·Bu,q, ,PU+Dq,'C ./:01-=1

(16)

(17)

Note that, due to the properties of (I), all users are separated

and each column in z· contain a signal that is due only to I,qp

one user and A WGN. Each line in zi.q. corresponds to

symbols sent over one sub carrier. We can therefore obtain the

u·h user symbols in only one column depending on p" . With

this observation, we can safely rewrite (16) and (17) as

z· =Au .·B _Au. ·B' +n'1"' (18) i,ql l,t "'.ql 2,1 u,q�

z�'l' = A�,i ,Bu,,,, + A�,i . B:,q, + D�, (19)

with z� a diagonal matrix obtained from the first column of I,qp

z· . pT . Since z" and A·.. are diagonal matrices, we may J,qp U I,Qp ),1 , write, for individual sub carrier k, zf,q, (k)=A�i(k).b •. q, (k)-h�.i(kp:q, (k)+n;, (k) (20)

<q, (k)=A�,i(k)'bu,q, (k)+A�.i(kp:,q, (k)+n�, (k) (21) Observe that, (20) and (21) are presented in identical form of

a single user STBC over a fading channel with two transmit antennas first proposed by Alamouti [12). With this observation, any decoding method known for the system proposed by Alamouti is applicable here. This also implies that, any concatenation technique associating STBC scheme for single user may still be usable in our multi-user system.

To obtain better performance, we add an LDPC encoder after the binary source at the transmitter and a decoder after symbol demodulator at the receiver. Due to the previous observation, LDPC can be used to form a turbo equalizer as in (13). In this paper, we assess the performance of the LDPC code concatenated with our system and eliminate any existing performances floor before constructing a turbo system to furthermore increase the performance of overall system. LDPC decoder takes hard or soft values issued from the symbol demodulator. The index k will be discarded from now on to simplify the demonstration. The presentation below is therefore to be applied to each OFDM tones independently

!fwe dcfine R" =A"� ·z� +A". 'z'" 1+ 1.1 I,QI 2,1 l,q�

RU =Au�·zu -1I." .. z"' J,- 1,1 I,qi I,E I,q�

(22)

(23)

user symbols (bu.q, ,b.,q,} can be extracted from (20)-(21) by

[ N ] 2

• R�' -A . b b •. q, =argmin :S:I 1,+ I,ll 1

hEn � YjjJ [L:N

I II '12] . R -'). ·b

b",q: =arg'min i�I' 1,- I hEn '--.--'

Yj./.�

(24)

(25)

with r' [d j ] the extrinsic a posteriori LLR of the jib bit of 1 u,qp

b and )=il,"")mn..} is the number of bit necessary to u,qp 1 represent a symbol in the n constellation. Q} denotes the set

of symbols in the constellation for which the jib bit is "+ 1" and

0; is defined similarly. p(p) represents the a priori

probability of the symbol p. r;'p [d!,qp ] is the extrinsic a

priori LLR fed back from by the LDPC decoder from the

previous turbo iteration (if any) respectively. r�'p [d!,qp] is set

to ° when turbo iteration is not used or at the first iteration of the turbo system.

III. SIMULATION RESULTS In this section, we present some simulation results to

illustrate our system performance. The performance of the system over perfectly estimated Rayleigh multi-path channel using fully orthogonal spreading signature (Walsh Hadamard) is investigated. The number of transmit and receive antennas are fixed to two and one respectively. 8PSK modulation is used. Of OM subsystem has 128 tones. At least 50,000,000 information bits have been simulated for each user. We idealize within our simulation that, perfect channel state information of each user is available to the receiver, along with perfect sample timing and perfect frequency synchronization. The users are quasi synchronous.

We consider a multi-user system using Walsh-Hadamard spreading code in a multi-path Rayleigh channel environment. We voluntarily limit the spreading code length to 8. We simulate 8 users communicating synchronously to the receiver.

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In Fig. 6, we present the performance for some of the users over various multi path Rayleigh channel configuration. The channels between users and between transmit antennas are independent and uncorrelated to each other. The simulation results presented in Fig. 6 confirm that the performance of our proposed multiuser uplink system is comparable with single user STBC system over fading channel. This 'shows the ability of our multi-user system to achieve the same capacity of a single user STBC system.

We concatenate a LOPC code to increase the system performance without any turbo architecture. Irregular weight 3 binary LOPC with rate 0.5 and size 200x400 and 2000x4000 are used to evaluate the sysiem performance. Figure 7 shows the system performances when LOPC code 200x400 is used while Figure 8 shows the performances with LOPC 2000x4000. We observe in these two figures that the multi path diversity is not totally exploited. Furthermore we remarked that the performances between these two codes are quasi identical, which is somehow abnormal.

With this constatation, we decided to investigate the effect of an additional symbol interleaver to the performance of the system even though it is well known that LOPC codes have an intrinsic binary interleaver. As we can see in Figure 9 there is observable performance gain compared to Figure 8 after the insertion of the additional symbol interleaver. This suggests that the intrinsic LDPC binary interleaver may not be sufficient to obtain maximum performance in a multi carrier multipath space time diversity environment.

Figure \0 resumes the effect of the symbol interleaver to a user in a 5-tap Rayleigh fading channel. The introduction of the interleaver leads to a 3dB gain at bit-eTTor-rate (BER) equals to 10.3 when the 2000x4000 LOpe code is used. The LOpe code 2000x4000 is at ldB better than LOpe code 200x400.

,.'

.. '

�"�;!l:'1IC:Of(JM __ """"' • .a�� <.;.....;...i:l�

.... VW';·I1t5> _o.IW<11 .. �:z;:�: • _,.;'0",­. ........-� �� ., ...,;.eo�.�

� .. """'" i . �""'" __ ...... � !.mr .... ..-',� ... .....tor.:.6Q(,

__ � �:'lr.l ....... _J.:::-:;t;r

. "

Fig. 6: BER of multiuser user multi-carrier SrBC over various Rayleigh muhi-path channels (Walsh Code)

�»("(,I/ ...... _ ....... tt"'C .. , .... _M.to.'JlI_.OIDW"""W-"'�_

ID-'f"""4 .. • ..... 1OGo ... l:IOd1f·C--'l-""' .... _"""_-....... II ......... -

10' ...... _'·1"' . ....... """,,' � to(' "._ �,...,I�·t�

• �""'I t.!UI ... ' .. ...-:-;..! .. • qj.Iw·M ....

II' • J"":; ��., " ,,-.:�� • _:�1", 4 ..... ; "1'.�. · _ ...... :-.. , .. .. ,,'Or':""'KQ-

"'!-, -�'---:---!---:--=----:;---'!.

Figure 7 : Performance of the system when LDPC code sized 200x400 is concatenated to the system over various muttipath channels without any

additional interleaver ...... .....-..... _ .......... :&1!K:.-W-__ ,:i\!I...."., .. O,r-.._....-__ ...... '�r·'-=..:;-=-='..:;""".;;. ... ;;;;..-=;;.; ..... =-=,..:..;:-;:;:.;-==··:.:;,...c:: .. :..:-;::::..:;;

,.'

10'

___ " �iItI ..... _(:0 ... • .,,- --_1). .....

... ..--,- ... '.·_1"i., · --, ..... '"

.. _1�1 ... II' ....... l1 .....

"'_'�""'" � _1 .. i. • -�I>'" ,. _�"l. " .. �.-=..;.;.::'---::------::------'!

Figure 8 : Perfonnance of the system when LDPC code sized 2000x4000 is concatenated to the system over various multipath channel without any

additional interleaver

�...-..� ............. .....,.."fl!lC .. ., __ lll-l""'"OI[]U_W_t-* .....

II)' wt�:llUlo4llil1)tQjO(: __ IIIII-.._ ... _' ___ .. .:loIl;o,...;.�

,,'

,,'

'0'

,{I' ::: =� �.:: __ 1:)1 ..

... ··_1.· .... I'"� ._'''\0000l0,

-.... _,,,,... ._::tl .... ... _�1'"

11" ........... ,...,., " -,.� ... • -;:.�* ... .. _:i'.'� '.'!-, -""-!c=--:--:---:----!--=--""*'--'! .

Figure 9: Perfonnance of the system when LDPC code sized 2000x4000 is concatenated to the system over various multipath channels with large

additional symbol interleaver added

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fflooc( .. _...-.-......-............. _ ........ .J.Jt(..(IoJI)I,I.....-­

'Vr-_-�'����'�'n����.���������������.-__ -,

,,' ,,' ,,'

\ \

:.... !i 11IIl� " .... _ ............... I.Of'I:I:IOIbtOe>

--_ ..... '""-'"l()1"1:��.oIICI1 _ ......... �'�IJIIFh_J ...- �t��� " ';-, ----T--�,,;__--"7---;---'-:;:---"i.

� ....

Figure 10 : EITect of the the additional interleaver for a user in a 5-tap Rayleigh channel

IV. CONCLUSION We proposed in this paper a new framework for multiuser

system over frequency selective channel for uplink system with space time diversity. We have shown that, for each user, the decoding problem is reduced to a single user case of the STBC. Hence, any decoding method known to conventional STBC may be applied here. We have also point out that any concatenation technique known associating STBC scheme for single user may still be feasible in our multi-user system. Our architecture simplifies multi-user system designs associating STBC. Computer simulation shows that our proposal can achieve the single user STBC performance in fading or multi­path channel with a relatively low complexity decoding. Furthermore, the receiver proposed need only one receiver antenna to decode all users and more receiver antennas can be used to improve the space diversity just like single user STBC systems.

Performance of the system when LDPC code is used as channel code is investigated. We observe significant performance improvement when an additional large symbol interleaver is added to the system after the symbol modulator (and before symbol demodulator respectively). This confirms the same trend observed in [10] with a space frequency diversity system.

Since our multiuser system can be decoupled to individual subsystem, we suspect that the additional symbol interleaver is needed if STBC is used over multiple carrier or when the receiver uses the frequency domain equalizer techniques.

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[2] A. Stamoulis. N. AI-Ohahir and A.R. Calderbank "Further results on interference Cancellation for Space-Time Block Coded Systems". Proc. Asilomar Conference on Signals. Systems and Computers, Nov. 2001

[3] Ayman F. Naguib, "Combined Interference Suppression and Frequency Domain Equalization for Space-Time Block Coded Transmission", ICC2003, May 2003

[4] Zhiqiang Liu; Giannakis, G.B., "Space.time block·coded multiple access through frequency-selective fading channels" , IEEE Trans. On Comm. Vol 49-6, pp: 1033-1044, June 2001,

[5] Zigang Yang, Ben Lu, and Xiaodong Wang. "Bayesian Monte Carlo Multi-user Receiver for Space-Time Coded Multi.earrier COMA Systems", IEEE Journal On Selected Areas In Communications. vol. 19-8, pp" 1625-1637, August 2001

[6] A. Stamoulis, Z. Liu. G.B. Giannakis, "Space time block coded OFOMA with linear precoding for multi rate service", IEEE Trans. On Signal Processing, vol. 50, pp 119 - 129, Jan. 2002

17] Baum. K.L.; Thomas, T.A.; Yook, F.W.; Nang;a, Y, "Cyclic-prefix COMA: an improved transmission method for broadband DS-COMA cellular systems",.WCNC 2002, March 2002

[8] Vook, F.W.; Thomas, T.A.; Baum, K.L, .. Cyclic-prefix COMA with antenna diversity", VTC Spring 2002, May 2002

[9] AuITray, 1.M.; Helard, J.F., "Performance of multi.eamer COMA technique combined with space-time block coding over Rayleigh channel", Spread Spectrum Techniques and Applications, 2002 IEEE Seventh International Symposium on , Sept. 2002

(10] MJ Syed, G. Ferre. V. Meghdadi, J.P. Canees, "Performances of LOPC based multi-user space frequency diversity system design for uplink multi-carrier COMA", 9'" International Conference On Communication Systems, Sept. 2004, Singapore

[Ill v. Tarokh, H. Jafarkhani, and R. A. Calderbank, "Space-Time Block Codes From Orthogonal Designs," IEEE Trans. Inform. Theory, vol. 45, pp. 1456-1467, July 1999"

(12] Siavash M. Alamouti, "A simple transmit diversity technique for wireless communications ", IEEE Journal of Selected Areas In Communications. vol 16-8 pp, 1451-1458, Oct 1998

[13] Ben Lu, Xiaodong Wang and Krishna R. Narayanan, "LOPC-Based Space-Time Coded OFDM Systems Over Correlated Fading Channels: Performance Analysis and Receiver Design", IEEE Tran. on Camm, vol. 50, pp74-88, Jan 2002

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