102 CHINESE OPTICS LETTERS / Vol. 7, No. 2 / February 10, 2009
A new family of two-dimensional triple-codeweight
asymmetric optical orthogonal code for OCDMA networks
Hongxi Yin (
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1∗
, Wei Liang (
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2
, Le Ma (
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, and Liqiao Qin (
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2
1
School of Electronic and Information Engineering, Dalian University of Technology, Dalian 116023
2
State Key Laboratory on Advanced Optical Communication Systems and Networks,
School of Electronics Engineering and Computer Science, Peking University, Beijing 100871
∗
E-mail: hxyin@pku.edu.cn
Received May 22, 2008
A new generation algorithm of two-dimensional triple-codeweight asymmetric optical orthogonal codes for
optical code division multiple access (OCDMA) networks is proposed. The code cardinality is obtained
and the error-probability performance for corresponding OCDMA system is analyzed. The codes with
two constraints (i.e., auto- and cross-correlation properties) being unequal are taken into account. On
the premise of fixed system resources, the code cardinality can be significantly improved. By analysis
of the error-probability performance, it is shown that the codes with different parameters have different
performances. Therefore, this type of codes can be applied to support diverse quality of service (QoS)
and satisfy the quality requirement of different multimedia or distinct users, and simultaneously make the
better use of bandwidth resources in optical networks.
OCIS codes: 060.1155, 060.2360, 060.4230.
doi: 10.3788/COL20090702.0102.
Optical code division multiple access (OCDMA) has been
considered as a competitive candidate for the multiple ac-
cess scheme in the future all-optical networks, especially
optical access networks, due to its attractive features such
as asynchronous access, dynamic bandwidth assig nment,
ability to support multimedia serv ice s, bursty traffic,
and so on. The user address code with better perfor-
mance is the basis for implementing an OCDMA net-
work. The result in previous work on optical orthogonal
codes (OOCs) considers the code with the same auto -
and cross-correlation constraints, until a new asymmet-
ric OOC has been developed
[1]
. The two constraints
have different effects on a system performance, because
the auto-correlation constraint contributes only to sys-
tem synchronization and the cro ss-correlation constraint
affects both synchronization and operation. According to
the distinction between these two cons traints, Yang et al.
developed a new algorithm to generate one-dimensional
(1D) constant-weight OOC with unequal correlation con-
straints (i.e., λ
a
> λ
c
)
[1]
through letting the auto-
correlation constra int exceed the cross-correlation con-
straint, which can ensure the system dependability by
improving the code cardinality.
To suppor t diverse quality of service (QoS) require-
ments in OCDMA networks, a double-codeweight OOC
technique
[2]
was propose d. However, this double-weight
OOC only supports two classes of services and cannot
satisfy QoS of different multimedia (e.g., data, voice, a nd
video). In addition, the codes mentioned above are all 1D
codes. Although their cardinalities have bee n improved,
compared with that of 1D symmetric code, they still have
some defects such as smaller cardinalities and worse cor-
relation performances.
In this letter, we extend the theories of 1D asymmet-
ric OOC and variable-weight OOC, and break through
the limitation of double-codeweight. As a result, a new
family of triple-codeweight 1D OO C is obtained, which
acts as time spreading pattern. Meanwhile, we em-
ploy one-coincident frequency-hopping code (OCFHC)
as wavelength-hopping pattern
[3]
and then a new two-
dimensional (2D) tr iple-codeweight asymmetric OOC
is gained. Using this code in OCDMA network, the
different Q oS requirements for different multimedia or
distinct users can be satisfied. This scheme can make
the better use of network resources so that 2 D triple-
codeweight asymmetric OOC has the potential to be
widely applied.
According to the effect of the two constrains on
system pe rformance, in order to improve code car-
dinality, the auto-correlation constraint of 1D OOC
is relaxed such that we can construct a triple-
codeweight code where the c odewords with large weights
have auto-correla tion c onstraints equal to 2 and the
codewords with smaller weights still keep auto- and
cross-correlation of at most one. By extending
double-codeweight c odewords to triple-codeweight code-
words, an (n, {w
l
, w
m
, w
s
}, {2, 1, 1}, 1, D) 1D OOC can
be obtained, where “l” represents large codeweight,
“m” indica tes medium codeweight, “s” signifies small
codeweight, and D = {t
0
/(t
0
+ t
1
+ t
2
), t
1
/(t
0
+ t
1
+ t
2
),
t
2
/(t
0
+ t
1
+ t
2
)} with t
0
, t
1
, and t
2
denoting the
numbers of codewords with large, medium, and s mall
codeweights, respectively. The small codeweight w
s
= w,
medium codeweig ht w
m
= w + 1, and large codeweight
w
l
= 2w, are chosen, and then the set of codeweight is
W = {2w, w + 1, w}. The 1D triple-codeweight code is
constructed as follows.
Let w = 2m + 1 and choose n to be a prime number
such that n = 2w
2
t
0
+ (w + 1)wt
1
+ w(w − 1)t
2
. If r
denotes the greatest common divisor of t
0
, t
1
, and t
2
, let
α be a primitive element of the Galois field GF (n) such
that
1671-7694/2009/020102-04
c
2009 Chinese Optics Letters