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3632 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 26, NO. 22, NOVEMBER 15, 2008

Design and Analysis of 2-D Codes With theMaximum Cross-Correlation Value

of Two for Optical CDMAJen-Hao Tien, Guu-Chang Yang , Senior Member, IEEE , Cheng-Yuan Chang , Member, IEEE , and

Wing C. Kwong , Senior Member, IEEE

Abstract—In this paper, a new family of two-dimensional (2-D)optical codes with the maximum cross-correlation value of two isconstructed and analyzed for optical code-division multiple access.Our 2-D codes employ wavelength hopping, controlled by the per-mutations of “synchronized” prime sequences, onto the pulses of a time-spreading optical orthogonal code (OOC). The new con-struction supports larger code cardinality (for more subscribers)and heavier code weight (for better code performance) without in-creasing the code length or number of wavelengths. Under cer-tain conditions, our analysis shows that the new codes can performbetter than our multiple-wavelength OOCs, which have cross-cor-relation values of at most one.

Index Terms—Optical code-division multiple access, opticalorthogonal code, time spreading, two-dimensional optical codes,wavelength hopping.

I. INTRODUCTION

O

PTICAL code-division multiple access (O-CDMA)

is currently receiving renewed attention due to the

advancement of two-dimensional (2-D) coding techniques,which combine wavelength hopping and time spreading in

optical codes [1]–[5]. Two-dimensional optical codes with

low cross-correlation values can support more subscribers

and simultaneous users than one-dimensional (1-D) optical

codes, such as the prime codes [3] and optical orthogonal codes

(OOCs) [6], for a given code length. The study of 2-D optical

codes was traditionally concentrated on the constructions of

code matrices with the cross-correlation values of at most

one in order to minimize multiple-access interference (MAI)

[1]–[5]. However, this kind of construction significantly re-

stricts code cardinality. It is known that we can support larger

Manuscript received September 14, 2007; revised April 7, 2008. Currentversion published January 28, 2009. This work was supported in part bythe National Science Council of the Republic of China under Grant NSC95-2221-E-005-023-MY3, in part by the Ministry of Education, Taiwan,R.O.C., under the ATU plan, in part by the U.S. Defense Advanced ResearchProjects Agency under Grant MDA972-03-1-0006, and in part by the Presi-dential Research Award and Faulty Development and Research Grants, HofstraUniversity.

J.-H. Tien and G.-C. Yang are with the Department of Electrical Engineering,National Chung-Hsing University, Taichung 402, Taiwan, R.O.C. (e-mail:[email protected]).

C.-Y. Chang is with the Department of Electrical Engineering, NationalUnited University, Miaoli, Taiwan, R.O.C. (e-mail: [email protected]).

W. C. Kwong is with the Department of Engineering, Hofstra University,Hempstead, NY 11549 USA (e-mail: [email protected]).

Digital Object Identifier 10.1109/JLT.2008.925029

TABLE ISYNCHRONIZED PRIME SEQUENCES OVER GF(5)

code cardinality and, in turn, more subscribers by relaxing the

maximum cross-correlation value, but this means larger MAI

as well [3], [6]–[11].

In [7], Mashhadi and Salehi computed the optimal values of

the code weight and maximum cross-correlation value that

minimize the error probability of optical codes for given code

length and cardinality. They concluded that the optimal value of

should be either two or three, and these optical codes weremorebeneficialthan optical codes,from a practical point

of view. It is because the former support larger code cardinality

with slightly worsening in code performance (or error proba-

bility), according to their analysis in [7]. As a result,

codes provide a better compromise in terms of code cardinality

and error probability than optical codes.

Nevertheless, previous work in the design of 2-D codes over-

looked the fact that larger cross-correlation values would allow

us to pack more pulses (i.e., heavier code weight) into code ma-

trices, resulting in higher autocorrelation peaks. Higher autocor-

relation peaks mean better discrimination against MAI and, in

turn, give better code performance. Therefore, by relaxing ,

we now have the question of whether larger MAI or heavier codeweight has a stronger effect in terms of code performance.

In Section II of this paper, we construct a new class of 2-D

optical codes by relaxing the maximum cross-correlation value

from one to two in order to increase the code weight and

cardinality. In Section III, our performance analysis shows that

heavier code weight supported by the new codes re-

sults inbetter codeperformancethan our multiple-wave-

length OOCs (MWOOCs) [5] under certain conditions and, at

the same time, supports more possible subscribers. This contra-

dicts a common belief that codes create stronger MAI

and should always perform worse than codes for the

benefit of achieving larger code cardinality.

0733-8724/$25.00 © 2008 IEEE



TIEN et al.: 2-D CODES WITH MAXIMUM CROSS-CORRELATION VALUE OF TWO FOR OPTICAL CDMA 3633

TABLE IICODE MATRICES OF LENGTH 13 AND FIVE WAVELENGTHS BASED ON THE SYNCHRONIZED PRIME SEQUENCES OVER GF(5)

AND THE CODEWORD 1100010010001 FROM THE (13,5,2,1) TIME-SPREADING OOC

II. CONSTRUCTION OF 2-D CODES

An 2-D optical code is a family of (0,1)

matrices with the number of wavelengths , code length , code

weight , maximum autocorrelation sidelobe , and maximum

cross-correlation value , such that we have the following.

• Autocorrelation: For any code matrix

in the 2-D code, the periodic autocorrelation side-

lobes are bounded by a positive integer , such that

for any integer delay

, where is an element of at

the th row and th column and “ ” denotes a modulo-

addition.

• Cross-correlation: For any two distinct matrices

and in the 2-D optical code, the pe-

riodic cross-correlation function is bounded by a positive

integer , such that for

any , where is an element in

at the th row and th column.

Inessence, our new ( 2,2) 2-D optical codes arecon-

structed by first choosing a ( 2,1) one-dimensional (1-D)OOC of length [6] as the time-spreading code. Afterwards,

wavelength hopping is added by assigning wavelengths to the

pulses of the time-spreading OOC algebraically. Wavelength as-

signment is determined by the “synchronized” prime sequences

[3], as shown in the following.

The synchronized prime sequences over Galois field (GF)

are obtained from

, where , , and are all in GF , is

a prime number, “ ” denotes a modulo- multiplication, and

“ ” denotes a modulo- addition. The synchronized prime

sequences can be classified in groups, indexed by . Each

prime sequence [3] with is used as a seed to generateother sequences in its group, resulting in a total of syn-

chronized prime sequences. This, in turn, gives permutations

for assigning wavelengths to the pulses of the time-spreading

OOC. For example, Table I shows the synchronized

prime sequences over GF(5). Table II shows the 25 (5

13,5,2,2) code matrices, originated from the (13,5,2,1) 1-D

OOC, 1100010010001, [4] with the wavelength indexes fol-

lowing the synchronized prime sequences of GF(5) in Table I.

The new codes support variable-weight operations because

the weight of the code matrices can be changed by simply drop-

ping pulses without worsening the cross-correlation functions.

As shown in Table I, for a code weight , only the first

th elements in each synchronized prime sequence are used forwavelength permutations. For example, if we want to lower the

weight of a code matrix from five to four, all we need to do is to

drop the last element in the corresponding synchronized prime

sequence in Table I and, in turn, drop the last pulse in the code

matrix in Table II. Since code weight determines the strength

of the autocorrelation peak, code matrices with heavier weight

have a better error probability and, thus, a greater chance to be

transmitted successfully. As result, the new codes are able to

support multimedia services in O-CDMA with services priori-tization [12].

When is a prime number, the elements within each syn-

chronized prime sequence, excluding those in group , are

all distinct (e.g., see Table I). This property keeps the cross-cor-

relation functions of the new codes as low as possible (i.e.,

in our case). However, when is not a prime number,

some of the synchronized prime sequences will have repeated

elements owing to the multiplication property of Galois field.

These repeated elements worsen the cross-correlation functions.

In this case, if we want to keep in our 2-D codes, those

sequences with repeated elements need to be removed. In other

words, if a nonprime is used, the code cardinality may be re-

duced, depending on the actual values of and in use. The rule

of picking the desirable sequences for the case of a nonprime

was detailed in [13]. For example, when and , there

are valid permutations because all eight sequences

have their first two elements nonrepeating. If , there

are only valid permutations because there are only

four sequences with their first four elements nonrepeating. In

short, our code construction does not require to be a prime

number. However, a prime will always maximize the cardi-

nality and, at the same time, keep the cross-correlation values

of the new codes being bounded to at most two.

A. Cross-Correlation Property

It is important to note that the cross-correlation property

of the new codes changes with the group number (e.g., see

Table I). As proved in this section, the cross-correlation value

of code matrices originated from different groups is at most

one. However, code matrices originated from the same group

(i.e., the same codeword of the OOC) have cross-correlation

values of at most two.

B. Cardinality

Let be the cardinality upper bound of the

OOC, where is the code length, is the codeweight, is the maximum autocorrelation sidelobe, and is




TABLE IIIEXAMPLES OF OVERALL CARDINALITIES OF THE NEW 2-D CODES AND MWOOCs

the maximum cross-correlation value. The upper bound is de-

rived by multiplying to the Johnson bound in [6], such that

(1)

When compared to (1), the cardinality of ( 2,1) OOC in

[6] is asymptotically optimal because its cardinality is equal to

for odd

for even(2)

Equation (2) determines the number of time-spreading OOC

codewords that can be used in our new 2-D codes, for given

and .

As mentioned earlier, the number of synchronized prime se-

quences (e.g., Table I) that can be used in the wavelength per-

mutations is given by . The number of synchronized

prime sequences suitable for the permutations is maximized

(i.e., ) when is a prime number. For each codeword

of the OOC, the permutationalgorithm can generate

at most (e.g., Table II) code matrices. Therefore, the overall

cardinality of the new 2-D codes is given by

(3)

For comparison, the overall cardinality of the

MWOOCs [5] is given by ,

where in accordance

with (1). The MWOOCs have almost half the number of

code matrices of the new 2-D codes for a given because(for odd ) and 2( 1)

(for even ). Numerical examples for the cardinality compar-

ison of both codes are given in Table III.

Theorem I: The cross-correlation functions and autocorrela-

tion sidelobes of the new 2-D codes are both at most two. The

overall code cardinality is .

Proof: See Appendix I.

By Theorem 1, the maximum autocorrelation sidelobe of the

proposed 2-D codes worsens to at most two because each code

matrix from group 0 uses the same wavelength in its pulses. By

removing group 0, we can reduce the autocorrelation sidelobes

to zero, giving a class of ( 0,2) 2-D codes. However,

the number of synchronized prime sequences that can be usedfor the wavelength permutations is reduced to .

Theorem 2: From any group , the au-

tocorrelation sidelobe of the proposed 2-D codes is reduced to

zero. The overall cardinality of these ( 0,2) 2-D codes

becomes by scarifying the

matrices from group 0.Proof: The proof is similar to that of Theorem 1. Every

pulse in each code matrix of group is con-

veyed with distinct wavelengths such that

for and . Hence, the autocorrela-

tion sidelobes of the proposed 2-D codes become zero.

III. PERFORMANCE ANALYSES

In this section, we introduce a combinatorial method to an-

alyze the hard-limiting1 performance of the new 2-D

codes for an interference limited O-CDMA system. In general,

the code performance is determined by code parameters such as

weight, length, the number of wavelengths, and the maximumcross-correlation value [1]–[5].

Let and denote the probabilities of the desired code ma-

trix (originated from group 0 and , re-

spectively) getting one hit in a time slot when it correlates with

a code matrix in the code set. Also, let denote the proba-

bility of the desired code matrix (originated from group

) getting two hits in the cross correlation. (The

term “two hits” defines the situation when a time slot of the

desired code matrix is being hit by two interfering pulses at

the same time. This causes the cross-correlation function to be

two.) In the following derivations, we assume that the number

of wavelengths is , there are groups of synchro-nized prime sequences, and an ( 2,1) OOC of cardinality

is used in the new ( 2,2) 2-D codes.

Theorem 3: Let and be two distinct (0,1) code

matrices in the code set. The number of times of getting two hits

in their cross-correlation is at most for odd weight

and at most for even weight. Then, we have

(4)

1It is known that a hard-limiter can be placed at the front end of a receiverbefore correlation is performed in order to reduce the effects of MAI and thenear–far problem [2], [3], [14], [15], [18]. While the operation details of hard-

limiters can be found in [21], their basic function is to clip the output light in-tensity to a fixed level if the input light intensity at a time instant is greater thana preset threshold. Otherwise, the output of the hard-limiter is zero.




for odd weight. The derivation of for even weight follows the

rationale of that of odd weight in (4), such that

(5)

Proof: See Appendix II.

A. Hit Probabilities for Odd Weight

From Section II, the length of the new 2-D codes is

if is an odd integer. From

Appendix III, we then have

(6)

(7)

(8)

B. Hit Probabilities for Even Weight

From Section II, the length of the new 2-D codes is

if is an even integer. Similar to

Section III-A, we then have

(9)

(10)

(11)

C. Error Probability Derivation

Denoting as the probability of getting hits in a time slot

out of the maximum cross-correlation value of , we have [3],

[5]

(12)

(13)

(14)

The error probability of the new 2-D codes, based on

the combinatorial analysis with hard-limiting detection, is given

by [14, (16)]

(15)

where denotes the number of simultaneous users. To have

a good code performance, this error-probability equation indi-cates that should be large but should be small.

For comparison, the hard-limiting error probability of the

MWOOCs is given by [2], [13], [15], [16]

(16)

where ,

,and

were derived in [5].

The error-probability equations for 2-D codes have been

well developed for , and higher values [7], [14],

[18]–[20]. Basically, these equations are the same for 2-D codes

with the same value. The only difference is on the hit-prob-

ability equations [e.g., (4)–(14)] because they depend on the

parameters (i.e., maximum cross-correlation values, length,

weight, cardinality, and number of wavelengths) of the 2-D

codes in study. In short, if two families of 2-D codes have the

same parameters, they will perform identically. Nevertheless,

comparing the performances of various 2-D codes is

not the scope of this paper. Instead, this paper studies how wecan pack more pulses in our codes in order to achieve

better code performance and, at the same time, larger code

cardinality. For example, we compare the error probabilities of

the new codes with the MWOOCs of the same

length in Figs. 4 and 5 of Section IV and show that the new

codes can support better performance under certain conditions.

IV. NUMERICAL EXAMPLES

In Fig. 1, the error probability , from (15), of the new

codes is plotted against the number of simultaneous

users for various code length and code weight . Indicated

next to the curves are the ( 2,1) 1-D time-spreading OOCsand number of wavelengths used to generate the corre-

sponding 2-D codes. The (13,5,2,1) OOC, which can be equiv-

alently denoted by the time-slot positions [0,1,5,8,12], is shown

in the caption of Table II. Similarly, the time-slot positions of

the (19,6,2,1) and (27,7,2,1) OOCs are given by [1,7,8,11,12,18]

and [0,1,4,10,17,23,26], respectively. Also plotted in the figure

are the computer-simulation results, which are found matching

closely with the analytical results. To explain how the com-

puter simulation is performed, we use the (13,5,2,1) curve as

an example. The code matrix assigned to each user is arbitrarily

selected from all 25 possible code matrices constructed from

GF(5), as shown in Table II. The total number of data bits in-volved in the simulation ranges from 100 000 to 100 000 000,

depending on the targeting error probability.

Fig. 2 shows the error probability of the new 2-D codes versus

the number of simultaneous users for various code weight

, where , , and .

Fig. 3 shows the error probability of the new 2-D codes versus

the number of simultaneous users for various code length

, where and . From Figs. 1–3, the error

probability in general gets worse as increases but improves

with or .

Fig. 4 compares the error probabilities of the

MWOOCs, based on the ( 1,1) time-spreading OOCs [i.e.,

(16)] and our new 2-D codes, based on the ( 2,1)time-spreading OOCs [i.e., (15)], for various code length ,




Fig. 1. Error probability of the new 2-D codes versus the number of simulta-neous users K with various (n ; w ; 2,1) time-spreading OOCs.

Fig. 2. Error probability of the new 2-D codes versus the number of si-multaneous users K for various w , where n = 1 8 1 , m = p = 1 9 , and = 1 .

number of wavelengths , and code weight . In general,

the error probability gets worse as increases but improves

with , , or . For the same and , the performance of our new 2-D codes is worse than that of the MWOOCs. Nev-

ertheless, the new 2-D codes can have a larger for the same

, hence compensating for the worsening in the performance

due to a larger . For example, the new 2-D codes generated

by the (111,15,2,1) OOC has , while the MWOOCs

generated by the (111,11,1,1) OOC has only . When the

difference of code weight between the new 2-D codes and

MWOOCs is at least equal to three, the former performs better

than the latter for for the same and . As shown in

the figure, the performance difference increases with .

Fig. 5 compares the error probabilities of the MWOOCs,

based on the ( 1,1) time-spreading OOC, and our new

2-D codes, based on the time-spreading OOC, for, where is even in the new 2-D codes. In

Fig. 3. Error probability of the new 2-D codes versus the number of simul-taneous users K for various n , where w = 6 , m = p = 7 , and =

.

Fig. 4. Error probabilities of the new 2-D codes and MWOOCs versus thenumber of simultaneous users K for various code-weight difference w .

general, the error probability gets worse as increases but im-

proves with the number of wavelengths . It is important

to point out that the new 2-D codes support a larger for the

same because the time-spreading OOCs supports a largerwhen the maximum cross-correlation value is relaxed from one

to two. Furthermore, the increase in code weight is more than

enough to compensate for the worsening in MAI, resulting a

net gain in the code performance. In our numerical example,

the performance difference increases with because increasing

the number of available wavelengths reduces the probability of

getting two hits.

V. CONCLUSION

In this paper, we proposed a new family of 2-D optical codes

with the cross-correlation functions of at most two. The new

codes could achieve larger code cardinality and sup-port heavier code weight than the codes, without the




Fig. 5. Error probabilities of the new 2-D codes with even weight and theMWOOCs versus the number of simultaneous users K , for various p .

need of increasing the code length. The new codes were ana-

lyzed and compared to the MWOOCs. While the new

codes supported almost twice as many code matrices as

the MWOOCs, our numerical example showed that the heavier

code weight supported by the new codes resulted in better code

performance than the MWOOCs under certain conditions. This

contradicted a common belief that codes should always

perform worse than codes for the benefit of larger car-

dinality.

APPENDIX I

PROOF OF THEOREM 1

In this Appendix, the correlation properties of the proposed

2-D codes, given in Theorem 1, are derived. Since every

pulse within each code matrix from group 0 has the same

wavelength, there will be at most two pulses colliding in the

cross-correlations. This is due to the autocorrelation property

of the OOC that the maximum autocorrelation

sidelobe is two. For any groups other than group 0, every pulse

within a code matrix is conveyed with distinct wavelengths

such that their autocorrelation sidelobes are all zero. Therefore,

the maximum autocorrelation value of the proposed 2-D codes

is at most two if group 0 is included.In the following, we derive the cross-correlation property by

considering two distinct code matrices, say, and . If their

time delay is equal to zero, the cross-correlation value be-

comes less than or equal to one. It is because the cross-cor-

relation value is at most one for any two different prime se-

quences over GF . If , there are two cases to

consider. In the first case, the cross-correlation value becomes

less than or equal to one when the code matrices are from two

different codewords of the ( 2,1) OOC. It is because the

maximum cross-correlation value of the ( 2,1) OOC is one.

In the second case, the cross-correlation value is less than or

equal to two when the code matrices are from the same code-

word of the ( 2,1) OOC. It is because the maximum auto-correlation sidelobeof the ( 2,1) OOC istwo. Therefore,the

maximum cross-correlation value of the proposed 2-D codes is

at most two.

APPENDIX II

PROOF OF THEOREM 3

Let the 2-D code be defined as a collec-

tion of matrices [17]. Also, let

......

......

(17)

......

......

(18)

such that

and

. While and determine thepermutation of wavelengths, and

denote the time positions of binary ones in code matrices and

, respectively.

Let and represent the sets of relative cyclic pulse de-

lays associated with and , respectively, as defined in [17].

If any two elements from and are the same, then we

can derive the number of hits by the repeated cyclic pulse de-

lays of the code matrices. The set of relative cyclic pulse de-

lays of the code matrix with odd weight contains

repeated elements. Since each element will contribute 1 rel-

ative cyclic pulse delays with the other 1 elements, then the

cyclic shifts of the code matrix with odd weight give a total of

two hits. Therefore, the number of one hit is equal to

[6]. Then, for the desired

code matrix originated from group , the

probability of getting two hits is given by

(19)

The factor 1/2 comes from the assumption of equiprobable

on–off data bit transmission. The term represents the

number of possible time shifts in a code matrix of length . The

term 1 represents the total number of two hits seen

by the desired code matrix with odd weight . Since each

( 2,1) time-spreading OOC can generate code matrices,there are in total code matrices and, thus, up

to interferers in the denominators.

The set of relative cyclic pulse delays of the code matrix with

even weight is derived similar to that of the code matrix with

odd weight. From [6], the cyclic shifts of the code matrix with

even weight gives a total of (w 2) 2 two hits and one hit.

The derivation of with even weight follows the rationale of

that of with odd weight.

APPENDIX III

In this Appendix, we derive the hit probabilities of the new

2-D codes with odd weight. Assuming that the number of avail-able wavelengths is and the code weight of the ( 2,1)




time-spreading OOC is . The desired 2-D code matrices

originated from group 0 have

(20)

After simple manipulations, (6) can be obtained.

In (20), the assumption of on–off data-bit transmission with

equal probability gives the factor 1/2 to all four terms in the

braces. The factor 1 represents the number of possible time

shifts between the two code matrices of length . Since each

( 2,1) time-spreading OOC can generate up to code ma-

trices, there are code matrices in total and,

thus, up to interferers in the denominators.

The first term in the braces of (20) relates to the hit probability

of the desired code matrix from group 0 caused by an interfering

code matrix from different groups but using the same ( 2,1)

time-spreading OOC as the desired code matrix, and there is no

time shift between the two code matrices. The factor 1

represents the number of interfering code matrices contributing

one hit. The second term is derived similar to that of the first

term but with a time shift. The factor 1 1 represents

the number of interfering code matrices, which can contribute

one hit. The third and fourth terms relate to the hit probabilities

of the desired code matrix from group 0 caused by interferingcode matrix from group 0 and groups 1 to 1, respectively,

using a different ( 2,1) time-spreading OOC from the de-

sired code matrix.

For the desired code matrix originated from group

with the probability of getting one

hit, we have

(21)

After some manipulations, we finally have (7).

The derivation of follows the rationales of that of . The

first three terms in the braces of (21) relate to the hit prob-

abilities of the desired code matrix from group caused by

interfering code matrices originated from the same ( 2,1)

time-spreading OOC as that of the desired code matrix. The first

term represents the case that the desired and interfering code

matrices are aligned without any time shift. The second termrepresents the case that the interfering code matrix gives one

hit to the desired code matrix with a time shift and the inter-

fering code matrix comes from group 0. The third term rep-

resents the case that the interfering code matrix comes from

groups 1 to 1 and gives one hit with desired code matrix

with a time shift. The factor [i.e.,

( 1)

from Appendix II] represents the number of interfering codematrices, which can contribute one hit. The fourth term relates

to the hit probability of the desired code matrix from group

caused by interfering code matrices originated from a different

( 2,1) time-spreading OOC from that of the desired code

matrix. The derivation of with even weight follows the ra-

tionale of that of with odd weight. Moreover, the deriva-

tions of with odd weight and even weight are explained in

Appendix II.

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[19] C.-C. Hsu, Y.-C. Chang, G.-C. Yang, C.-L. Chang, and W. C. Kwong,“Performance analysis of 2-D optical codes without the chip-syn-chronous assumption,” IEEE J. Sel. Areas Commun., vol. 25, pp.135–143, Aug. 2007.

[20] C.-C. Hsu, G.-C. Yang, and W. C. Kwong, “Performance analysis of 2-D optical codes with arbitrary cross-correlation values under thechip-asynchronous assumption,” IEEE Commun. Lett., vol. 11, pp.170–172, Feb. 2007.

[21] C.-C.Hsu, G.-C. Yang, and W. C. Kwong, “Hard-limitingperformanceanalysis of 2-D optical codes under the chip-asynchronous assump-tion,” IEEE Trans. Commun., vol. 56, no. 5, pp. 762–768, May 2008.

Jen-Hao Tien received the B.S. degree in electricalengineering from National Chung-Hsing University,Taichung, Taiwan, R.O.C, in 2005, where he is cur-rently pursuing the M.S. degree in electrical engi-neering.

His research interests include optical communica-tions and wireless communications.

Guu-Chang Yang (S’88–M’92–SM’05) receivedthe B.S. degree from the National Taiwan University,Taipei, Taiwan, R.O.C., in 1985 and the M.S. andPh.D. degrees from the University of Maryland,College Park, MD, in 1989 and 1992, respectively,all in electrical engineering.

From 1988 to 1992, he was a Research Assistantwith the System Research Center, University of Maryland. In 1992, he joined the Faculty of NationalChung-Hsing University, Taichung, Taiwan, wherehe is currently a Professor in the Department of

Electrical Engineering. He was Chairman of the Department of ElectricalEngineering from 2001 to 2004. His research interests include wireless andoptical communication systems, spreading code designs, and applicationsof code-division multiple access. He coauthored a first-of-its-kind technical

book on optical code-division multiple access, Prime Codes with Applicationsto CDMA Optical and Wireless Networks (Norwood, MA: Artech House,2002) and contributed a chapter to Optical Code Division Multiple Access:

Fundamentals and Applications (Boca Raton, FL: Taylor & Francis, 2006).Dr. Yang was Chairman of the IEEE Information Theory Society Taipei

Chapter from 2003to 2005and Vice-Chairman of the IEEE Information Theory

Society Taipei Chapter from 1999 to 2000. He received the DistinguishedResearch Award from the National Science Council in 2004 and ExcellentYoung Electrical Engineering Award from the Chinese Institute of ElectricalEngineering in 2003. He also received the Best Teaching Awards from theDepartment of Electrical Engineering from National Chung-Hsing Universityfrom 2001 to 2004.

Cheng-Yuan Chang (S’04–M’07) received theB.S. degree from National Sun Yat-Sen University,Kaohsiung, Taiwan, R.O.C., in 1997 and the M.S.and Ph.D. degrees from National Chung-HsingUniversity, Taichung, Taiwan, in 2002 and 2007,respectively, all in electrical engineering.

In 2007, he joined the Faculty of National UnitedUniversity, Miaoli, Taiwan, where he is presently anAssistant Professor in the Department of ElectricalEngineering. His research interests include opticaland wireless communications.

Wing C. Kwong (S’88–M’92–SM’97) received the

B.S. degree from the University of California, SanDiego, in 1987 and the Ph.D. degree from PrincetonUniversity, Princeton, NJ, in 1992, both in electricalengineering.

In 1992, he joined the Faculty of Hofstra Uni-versity, Hempstead, NY, where he is presently aProfessor in the Department of Engineering. Hisresearch interests are centered on optical and wire-less communication systems and multiple-accessnetworks, optical interconnection networks, and

ultrafast all-optical signal processing techniques. He has published more than120 professional papers, chaired technical sessions, and served on technicalprogram committees in various international conferences. He has giveninvited seminars in various countries, such as Canada, Korea, and Taiwan.He coauthored a first-of-its-kind technical book on optical code-divisionmultiple access, Prime Codes with Applications to CDMA Optical and Wireless

Networks (Norwood, MA: Artech House, 2002) and contributed a chapter to

Optical Code Division Multiple Access: Fundamentals and Applications (BocaRaton, FL: Taylor & Francis, 2006).

Dr. Kwong is an Associate Editor of the IEEE TRANSACTIONS ON

COMMUNICATIONS. He received an NEC Graduate Fellowship from NECResearch Institute in 1991. He received the Young Engineer Award from theIEEE (Long Island chapter) in 1998.

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